(8x-11)(2x+6)5=180

Solution for (8x-11)(2x+6)5=180 equation:

(8x-11)(2x+6)5=180

We move all terms to the left:

(8x-11)(2x+6)5-(180)=0

We multiply parentheses ..

(+16x^2+48x-22x-66)5-180=0

We multiply parentheses

80x^2+240x-110x-330-180=0

We add all the numbers together, and all the variables

80x^2+130x-510=0

a = 80; b = 130; c = -510;
Δ = b2-4ac
Δ = 1302-4·80·(-510)
Δ = 180100
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:

$\sqrt{\Delta}=\sqrt{180100}=\sqrt{100*1801}=\sqrt{100}*\sqrt{1801}=10\sqrt{1801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-10\sqrt{1801}}{2*80}=\frac{-130-10\sqrt{1801}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+10\sqrt{1801}}{2*80}=\frac{-130+10\sqrt{1801}}{160}
$