(4x+2)(3x-7)=90

Solution for (4x+2)(3x-7)=90 equation:

(4x+2)(3x-7)=90

We move all terms to the left:

(4x+2)(3x-7)-(90)=0

We multiply parentheses ..

(+12x^2-28x+6x-14)-90=0

We get rid of parentheses

12x^2-28x+6x-14-90=0

We add all the numbers together, and all the variables

12x^2-22x-104=0

a = 12; b = -22; c = -104;
Δ = b2-4ac
Δ = -222-4·12·(-104)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-74}{2*12}=\frac{-52}{24}
=-2+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+74}{2*12}=\frac{96}{24}
=4
$