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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2-14x+5x+35)=0

We get rid of parentheses

-2x^2-14x+5x+35=0

We add all the numbers together, and all the variables

-2x^2-9x+35=0

a = -2; b = -9; c = +35;
Δ = b2-4ac
Δ = -92-4·(-2)·35
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*-2}=\frac{28}{-4}
=-7
$