(6x+4)(8x-6)=180

Solution for (6x+4)(8x-6)=180 equation:

(6x+4)(8x-6)=180

We move all terms to the left:

(6x+4)(8x-6)-(180)=0

We multiply parentheses ..

(+48x^2-36x+32x-24)-180=0

We get rid of parentheses

48x^2-36x+32x-24-180=0

We add all the numbers together, and all the variables

48x^2-4x-204=0

a = 48; b = -4; c = -204;
Δ = b2-4ac
Δ = -42-4·48·(-204)
Δ = 39184
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:

$\sqrt{\Delta}=\sqrt{39184}=\sqrt{16*2449}=\sqrt{16}*\sqrt{2449}=4\sqrt{2449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2449}}{2*48}=\frac{4-4\sqrt{2449}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2449}}{2*48}=\frac{4+4\sqrt{2449}}{96}
$