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

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

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

We multiply parentheses ..

5(+x^2+5x-2x-10)=0

We multiply parentheses

5x^2+25x-10x-50=0

We add all the numbers together, and all the variables

5x^2+15x-50=0

a = 5; b = 15; c = -50;
Δ = b2-4ac
Δ = 152-4·5·(-50)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-35}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+35}{2*5}=\frac{20}{10}
=2
$