(4x-5)(3x-2)=90

Solution for (4x-5)(3x-2)=90 equation:

(4x-5)(3x-2)=90

We move all terms to the left:

(4x-5)(3x-2)-(90)=0

We multiply parentheses ..

(+12x^2-8x-15x+10)-90=0

We get rid of parentheses

12x^2-8x-15x+10-90=0

We add all the numbers together, and all the variables

12x^2-23x-80=0

a = 12; b = -23; c = -80;
Δ = b2-4ac
Δ = -232-4·12·(-80)
Δ = 4369
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{-(-23)-\sqrt{4369}}{2*12}=\frac{23-\sqrt{4369}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{4369}}{2*12}=\frac{23+\sqrt{4369}}{24}
$