Mister Exam

Other calculators


20*x^2-21*x+22=17x^2-75x-218

20*x^2-21*x+22=17x^2-75x-218 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
    2                   2             
20*x  - 21*x + 22 = 17*x  - 75*x - 218
$$20 x^{2} - 21 x + 22 = 17 x^{2} - 75 x - 218$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$20 x^{2} - 21 x + 22 = 17 x^{2} - 75 x - 218$$
to
$$\left(- 17 x^{2} + 75 x + 218\right) + \left(20 x^{2} - 21 x + 22\right) = 0$$
This equation is of the form
$$a*x^2 + b*x + c = 0$$
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 3$$
$$b = 54$$
$$c = 240$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 3 \cdot 4 \cdot 240 + 54^{2} = 36$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = -8$$
Simplify
$$x_{2} = -10$$
Simplify
Vieta's Theorem
rewrite the equation
$$20 x^{2} - 21 x + 22 = 17 x^{2} - 75 x - 218$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 18 x + 80 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 18$$
$$q = \frac{c}{a}$$
$$q = 80$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -18$$
$$x_{1} x_{2} = 80$$
The graph
Sum and product of roots [src]
sum
-10 + -8
$$\left(-10\right) + \left(-8\right)$$
=
-18
$$-18$$
product
-10 * -8
$$\left(-10\right) * \left(-8\right)$$
=
80
$$80$$
Rapid solution [src]
x_1 = -10
$$x_{1} = -10$$
x_2 = -8
$$x_{2} = -8$$
Numerical answer [src]
x1 = -10.0
x2 = -8.0
x2 = -8.0
The graph
20*x^2-21*x+22=17x^2-75x-218 equation