(4x-9)(2x+6)=90

Solution for (4x-9)(2x+6)=90 equation:

(4x-9)(2x+6)=90

We move all terms to the left:

(4x-9)(2x+6)-(90)=0

We multiply parentheses ..

(+8x^2+24x-18x-54)-90=0

We get rid of parentheses

8x^2+24x-18x-54-90=0

We add all the numbers together, and all the variables

8x^2+6x-144=0

a = 8; b = 6; c = -144;
Δ = b2-4ac
Δ = 62-4·8·(-144)
Δ = 4644
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:

$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{129}}{2*8}=\frac{-6-6\sqrt{129}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{129}}{2*8}=\frac{-6+6\sqrt{129}}{16}
$