(3x+13)(8x+14)=180

Solution for (3x+13)(8x+14)=180 equation:

(3x+13)(8x+14)=180

We move all terms to the left:

(3x+13)(8x+14)-(180)=0

We multiply parentheses ..

(+24x^2+42x+104x+182)-180=0

We get rid of parentheses

24x^2+42x+104x+182-180=0

We add all the numbers together, and all the variables

24x^2+146x+2=0

a = 24; b = 146; c = +2;
Δ = b2-4ac
Δ = 1462-4·24·2
Δ = 21124
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:

$\sqrt{\Delta}=\sqrt{21124}=\sqrt{4*5281}=\sqrt{4}*\sqrt{5281}=2\sqrt{5281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(146)-2\sqrt{5281}}{2*24}=\frac{-146-2\sqrt{5281}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(146)+2\sqrt{5281}}{2*24}=\frac{-146+2\sqrt{5281}}{48}
$