(x-5)(7x+3)=0

Solution for (x-5)(7x+3)=0 equation:

(x-5)(7x+3)=0

We multiply parentheses ..

(+7x^2+3x-35x-15)=0

We get rid of parentheses

7x^2+3x-35x-15=0

We add all the numbers together, and all the variables

7x^2-32x-15=0

a = 7; b = -32; c = -15;
Δ = b2-4ac
Δ = -322-4·7·(-15)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-38}{2*7}=\frac{-6}{14}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+38}{2*7}=\frac{70}{14}
=5
$