(4n-2)(3n+8)=90

Solution for (4n-2)(3n+8)=90 equation:

(4n-2)(3n+8)=90

We move all terms to the left:

(4n-2)(3n+8)-(90)=0

We multiply parentheses ..

(+12n^2+32n-6n-16)-90=0

We get rid of parentheses

12n^2+32n-6n-16-90=0

We add all the numbers together, and all the variables

12n^2+26n-106=0

a = 12; b = 26; c = -106;
Δ = b2-4ac
Δ = 262-4·12·(-106)
Δ = 5764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5764}=\sqrt{4*1441}=\sqrt{4}*\sqrt{1441}=2\sqrt{1441}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1441}}{2*12}=\frac{-26-2\sqrt{1441}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1441}}{2*12}=\frac{-26+2\sqrt{1441}}{24}
$