Mister Exam

Other calculators

(-4x+7)(-x+5)=0

(-4x+7)(-x+5)=0 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] 
(-4*x + 7)*(-x + 5) = 0
(5−x)(7−4x)=0\left(5 - x\right) \left(7 - 4 x\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(5−x)(7−4x)=0\left(5 - x\right) \left(7 - 4 x\right) = 0
We get the quadratic equation
4x2−27x+35=04 x^{2} - 27 x + 35 = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=4a = 4
b=−27b = -27
c=35c = 35
, then
D = b^2 - 4 * a * c = 

(-27)^2 - 4 * (4) * (35) = 169

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=5x_{1} = 5
x2=74x_{2} = \frac{7}{4}
The graph
05-10-5101520-5001000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 7/4
x1=74x_{1} = \frac{7}{4} 
x2 = 5
x2=5x_{2} = 5 
x2 = 5
Sum and product of roots [src] 
sum
5 + 7/4
74+5\frac{7}{4} + 5 
=
27/4
274\frac{27}{4} 
product
5*7
---
 4
5⋅74\frac{5 \cdot 7}{4} 
=
35/4
354\frac{35}{4} 
35/4
Numerical answer [src] 
x1 = 5.0
x2 = 1.75
x2 = 1.75
The graph
(-4x+7)(-x+5)=0 equation
    © Mister Exam – Calculator