(6x-15)(8+x)=168

Solution for (6x-15)(8+x)=168 equation:

(6x-15)(8+x)=168

We move all terms to the left:

(6x-15)(8+x)-(168)=0

We add all the numbers together, and all the variables

(6x-15)(x+8)-168=0

We multiply parentheses ..

(+6x^2+48x-15x-120)-168=0

We get rid of parentheses

6x^2+48x-15x-120-168=0

We add all the numbers together, and all the variables

6x^2+33x-288=0

a = 6; b = 33; c = -288;
Δ = b2-4ac
Δ = 332-4·6·(-288)
Δ = 8001
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:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{889}}{2*6}=\frac{-33-3\sqrt{889}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{889}}{2*6}=\frac{-33+3\sqrt{889}}{12}
$