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

Solution for 5(x+7)(x-10)=0 equation:

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

We multiply parentheses ..

5(+x^2-10x+7x-70)=0

We multiply parentheses

5x^2-50x+35x-350=0

We add all the numbers together, and all the variables

5x^2-15x-350=0

a = 5; b = -15; c = -350;
Δ = b2-4ac
Δ = -152-4·5·(-350)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-85}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+85}{2*5}=\frac{100}{10}
=10
$