(5x+6)(9x-8)=180

Solution for (5x+6)(9x-8)=180 equation:

(5x+6)(9x-8)=180

We move all terms to the left:

(5x+6)(9x-8)-(180)=0

We multiply parentheses ..

(+45x^2-40x+54x-48)-180=0

We get rid of parentheses

45x^2-40x+54x-48-180=0

We add all the numbers together, and all the variables

45x^2+14x-228=0

a = 45; b = 14; c = -228;
Δ = b2-4ac
Δ = 142-4·45·(-228)
Δ = 41236
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:

$\sqrt{\Delta}=\sqrt{41236}=\sqrt{676*61}=\sqrt{676}*\sqrt{61}=26\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26\sqrt{61}}{2*45}=\frac{-14-26\sqrt{61}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26\sqrt{61}}{2*45}=\frac{-14+26\sqrt{61}}{90}
$