(X+4)(3x+2)=90

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

(X+4)(3X+2)=90

We move all terms to the left:

(X+4)(3X+2)-(90)=0

We multiply parentheses ..

(+3X^2+2X+12X+8)-90=0

We get rid of parentheses

3X^2+2X+12X+8-90=0

We add all the numbers together, and all the variables

3X^2+14X-82=0

a = 3; b = 14; c = -82;
Δ = b2-4ac
Δ = 142-4·3·(-82)
Δ = 1180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{295}}{2*3}=\frac{-14-2\sqrt{295}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{295}}{2*3}=\frac{-14+2\sqrt{295}}{6}
$