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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+20x-35=0

a = 15; b = 20; c = -35;
Δ = b2-4ac
Δ = 202-4·15·(-35)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-50}{2*15}=\frac{-70}{30}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+50}{2*15}=\frac{30}{30}
=1
$