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

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

(X+8)(3X+14)=180

We move all terms to the left:

(X+8)(3X+14)-(180)=0

We multiply parentheses ..

(+3X^2+14X+24X+112)-180=0

We get rid of parentheses

3X^2+14X+24X+112-180=0

We add all the numbers together, and all the variables

3X^2+38X-68=0

a = 3; b = 38; c = -68;
Δ = b2-4ac
Δ = 382-4·3·(-68)
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{565}}{2*3}=\frac{-38-2\sqrt{565}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{565}}{2*3}=\frac{-38+2\sqrt{565}}{6}
$