(6x+20)(8x-10)=180

Solution for (6x+20)(8x-10)=180 equation:

(6x+20)(8x-10)=180

We move all terms to the left:

(6x+20)(8x-10)-(180)=0

We multiply parentheses ..

(+48x^2-60x+160x-200)-180=0

We get rid of parentheses

48x^2-60x+160x-200-180=0

We add all the numbers together, and all the variables

48x^2+100x-380=0

a = 48; b = 100; c = -380;
Δ = b2-4ac
Δ = 1002-4·48·(-380)
Δ = 82960
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:

$\sqrt{\Delta}=\sqrt{82960}=\sqrt{16*5185}=\sqrt{16}*\sqrt{5185}=4\sqrt{5185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{5185}}{2*48}=\frac{-100-4\sqrt{5185}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{5185}}{2*48}=\frac{-100+4\sqrt{5185}}{96}
$