(6x+23)(2x+5)=180

Solution for (6x+23)(2x+5)=180 equation:

(6x+23)(2x+5)=180

We move all terms to the left:

(6x+23)(2x+5)-(180)=0

We multiply parentheses ..

(+12x^2+30x+46x+115)-180=0

We get rid of parentheses

12x^2+30x+46x+115-180=0

We add all the numbers together, and all the variables

12x^2+76x-65=0

a = 12; b = 76; c = -65;
Δ = b2-4ac
Δ = 762-4·12·(-65)
Δ = 8896
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:

$\sqrt{\Delta}=\sqrt{8896}=\sqrt{64*139}=\sqrt{64}*\sqrt{139}=8\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-8\sqrt{139}}{2*12}=\frac{-76-8\sqrt{139}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+8\sqrt{139}}{2*12}=\frac{-76+8\sqrt{139}}{24}
$