(7x-5)(-2x+5)=0

Solution for (7x-5)(-2x+5)=0 equation:

(7x-5)(-2x+5)=0

We multiply parentheses ..

(-14x^2+35x+10x-25)=0

We get rid of parentheses

-14x^2+35x+10x-25=0

We add all the numbers together, and all the variables

-14x^2+45x-25=0

a = -14; b = 45; c = -25;
Δ = b2-4ac
Δ = 452-4·(-14)·(-25)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-25}{2*-14}=\frac{-70}{-28}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+25}{2*-14}=\frac{-20}{-28}
=5/7
$