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Identical expressions
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Similar expressions
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(9y-2)(2.1-7y)=0 equation
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The solution
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[src]
/21 \
(9*y - 2)*|-- - 7*y| = 0
\10 /
$$\left(\frac{21}{10} - 7 y\right) \left(9 y - 2\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(\frac{21}{10} - 7 y\right) \left(9 y - 2\right) = 0$$
We get the quadratic equation
$$- 63 y^{2} + \frac{329 y}{10} - \frac{21}{5} = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -63$$
$$b = \frac{329}{10}$$
$$c = - \frac{21}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = \frac{2}{9}$$
$$y_{2} = \frac{3}{10}$$
$$\left(\frac{21}{10} - 7 y\right) \left(9 y - 2\right) = 0$$
We get the quadratic equation
$$- 63 y^{2} + \frac{329 y}{10} - \frac{21}{5} = 0$$
This equation is of the form
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -63$$
$$b = \frac{329}{10}$$
$$c = - \frac{21}{5}$$
, then
D = b^2 - 4 * a * c =
(329/10)^2 - 4 * (-63) * (-21/5) = 2401/100
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = \frac{2}{9}$$
$$y_{2} = \frac{3}{10}$$
Sum and product of roots
[src]
sum
2/9 + 3/10
$$\frac{2}{9} + \frac{3}{10}$$
=
47 -- 90
$$\frac{47}{90}$$
product
2*3 ---- 9*10
$$\frac{2 \cdot 3}{9 \cdot 10}$$
=
1/15
$$\frac{1}{15}$$
1/15