(3a+4)(6a-4)=90

Solution for (3a+4)(6a-4)=90 equation:

(3a+4)(6a-4)=90

We move all terms to the left:

(3a+4)(6a-4)-(90)=0

We multiply parentheses ..

(+18a^2-12a+24a-16)-90=0

We get rid of parentheses

18a^2-12a+24a-16-90=0

We add all the numbers together, and all the variables

18a^2+12a-106=0

a = 18; b = 12; c = -106;
Δ = b2-4ac
Δ = 122-4·18·(-106)
Δ = 7776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36\sqrt{6}}{2*18}=\frac{-12-36\sqrt{6}}{36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36\sqrt{6}}{2*18}=\frac{-12+36\sqrt{6}}{36}
$