(3x+6)(9x-8)=142

Solution for (3x+6)(9x-8)=142 equation:

(3x+6)(9x-8)=142

We move all terms to the left:

(3x+6)(9x-8)-(142)=0

We multiply parentheses ..

(+27x^2-24x+54x-48)-142=0

We get rid of parentheses

27x^2-24x+54x-48-142=0

We add all the numbers together, and all the variables

27x^2+30x-190=0

a = 27; b = 30; c = -190;
Δ = b2-4ac
Δ = 302-4·27·(-190)
Δ = 21420
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:

$\sqrt{\Delta}=\sqrt{21420}=\sqrt{36*595}=\sqrt{36}*\sqrt{595}=6\sqrt{595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{595}}{2*27}=\frac{-30-6\sqrt{595}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{595}}{2*27}=\frac{-30+6\sqrt{595}}{54}
$