(6x)(x-23)=180

Solution for (6x)(x-23)=180 equation:

(6x)(x-23)=180

We move all terms to the left:

(6x)(x-23)-(180)=0

We multiply parentheses

6x^2-138x-180=0

a = 6; b = -138; c = -180;
Δ = b2-4ac
Δ = -1382-4·6·(-180)
Δ = 23364
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:

$\sqrt{\Delta}=\sqrt{23364}=\sqrt{36*649}=\sqrt{36}*\sqrt{649}=6\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-6\sqrt{649}}{2*6}=\frac{138-6\sqrt{649}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+6\sqrt{649}}{2*6}=\frac{138+6\sqrt{649}}{12}
$