(89-6x)(3x+62)=180

Solution for (89-6x)(3x+62)=180 equation:

(89-6x)(3x+62)=180

We move all terms to the left:

(89-6x)(3x+62)-(180)=0

We add all the numbers together, and all the variables

(-6x+89)(3x+62)-180=0

We multiply parentheses ..

(-18x^2-372x+267x+5518)-180=0

We get rid of parentheses

-18x^2-372x+267x+5518-180=0

We add all the numbers together, and all the variables

-18x^2-105x+5338=0

a = -18; b = -105; c = +5338;
Δ = b2-4ac
Δ = -1052-4·(-18)·5338
Δ = 395361
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:

$\sqrt{\Delta}=\sqrt{395361}=\sqrt{81*4881}=\sqrt{81}*\sqrt{4881}=9\sqrt{4881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-9\sqrt{4881}}{2*-18}=\frac{105-9\sqrt{4881}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+9\sqrt{4881}}{2*-18}=\frac{105+9\sqrt{4881}}{-36}
$