(7x+6)(6x-7)=90

Solution for (7x+6)(6x-7)=90 equation:

(7x+6)(6x-7)=90

We move all terms to the left:

(7x+6)(6x-7)-(90)=0

We multiply parentheses ..

(+42x^2-49x+36x-42)-90=0

We get rid of parentheses

42x^2-49x+36x-42-90=0

We add all the numbers together, and all the variables

42x^2-13x-132=0

a = 42; b = -13; c = -132;
Δ = b2-4ac
Δ = -132-4·42·(-132)
Δ = 22345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{22345}}{2*42}=\frac{13-\sqrt{22345}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{22345}}{2*42}=\frac{13+\sqrt{22345}}{84}
$