(2x+5)(6x+5)=180

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

(2x+5)(6x+5)=180

We move all terms to the left:

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

We multiply parentheses ..

(+12x^2+10x+30x+25)-180=0

We get rid of parentheses

12x^2+10x+30x+25-180=0

We add all the numbers together, and all the variables

12x^2+40x-155=0

a = 12; b = 40; c = -155;
Δ = b2-4ac
Δ = 402-4·12·(-155)
Δ = 9040
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:

$\sqrt{\Delta}=\sqrt{9040}=\sqrt{16*565}=\sqrt{16}*\sqrt{565}=4\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{565}}{2*12}=\frac{-40-4\sqrt{565}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{565}}{2*12}=\frac{-40+4\sqrt{565}}{24}
$