(5x-6)(7x+6)=0

Solution for (5x-6)(7x+6)=0 equation:

(5x-6)(7x+6)=0

We multiply parentheses ..

(+35x^2+30x-42x-36)=0

We get rid of parentheses

35x^2+30x-42x-36=0

We add all the numbers together, and all the variables

35x^2-12x-36=0

a = 35; b = -12; c = -36;
Δ = b2-4ac
Δ = -122-4·35·(-36)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-72}{2*35}=\frac{-60}{70}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+72}{2*35}=\frac{84}{70}
=1+1/5
$