(2x+5)(8x+5)=180

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

(2x+5)(8x+5)=180

We move all terms to the left:

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

We multiply parentheses ..

(+16x^2+10x+40x+25)-180=0

We get rid of parentheses

16x^2+10x+40x+25-180=0

We add all the numbers together, and all the variables

16x^2+50x-155=0

a = 16; b = 50; c = -155;
Δ = b2-4ac
Δ = 502-4·16·(-155)
Δ = 12420
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:

$\sqrt{\Delta}=\sqrt{12420}=\sqrt{36*345}=\sqrt{36}*\sqrt{345}=6\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-6\sqrt{345}}{2*16}=\frac{-50-6\sqrt{345}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+6\sqrt{345}}{2*16}=\frac{-50+6\sqrt{345}}{32}
$