(3x+4)(-9x+6)=-8

Solution for (3x+4)(-9x+6)=-8 equation:

(3x+4)(-9x+6)=-8

We move all terms to the left:

(3x+4)(-9x+6)-(-8)=0

We add all the numbers together, and all the variables

(3x+4)(-9x+6)+8=0

We multiply parentheses ..

(-27x^2+18x-36x+24)+8=0

We get rid of parentheses

-27x^2+18x-36x+24+8=0

We add all the numbers together, and all the variables

-27x^2-18x+32=0

a = -27; b = -18; c = +32;
Δ = b2-4ac
Δ = -182-4·(-27)·32
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{105}}{2*-27}=\frac{18-6\sqrt{105}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{105}}{2*-27}=\frac{18+6\sqrt{105}}{-54}
$