9x^2+4x-6x=-5x+8

Solution for 9x^2+4x-6x=-5x+8 equation:

9x^2+4x-6x=-5x+8

We move all terms to the left:

9x^2+4x-6x-(-5x+8)=0

We add all the numbers together, and all the variables

9x^2-2x-(-5x+8)=0

We get rid of parentheses

9x^2-2x+5x-8=0

We add all the numbers together, and all the variables

9x^2+3x-8=0

a = 9; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·9·(-8)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*9}=\frac{-3-3\sqrt{33}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*9}=\frac{-3+3\sqrt{33}}{18}
$