(x-7)(-2x+10)=0

Solution for (x-7)(-2x+10)=0 equation:

(x-7)(-2x+10)=0

We multiply parentheses ..

(-2x^2+10x+14x-70)=0

We get rid of parentheses

-2x^2+10x+14x-70=0

We add all the numbers together, and all the variables

-2x^2+24x-70=0

a = -2; b = 24; c = -70;
Δ = b2-4ac
Δ = 242-4·(-2)·(-70)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4}{2*-2}=\frac{-20}{-4}
=+5
$