5x-3x^2=-8-6x

Solution for 5x-3x^2=-8-6x equation:

5x-3x^2=-8-6x

We move all terms to the left:

5x-3x^2-(-8-6x)=0

We add all the numbers together, and all the variables

-3x^2+5x-(-6x-8)=0

We get rid of parentheses

-3x^2+5x+6x+8=0

We add all the numbers together, and all the variables

-3x^2+11x+8=0

a = -3; b = 11; c = +8;
Δ = b2-4ac
Δ = 112-4·(-3)·8
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{217}}{2*-3}=\frac{-11-\sqrt{217}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*-3}=\frac{-11+\sqrt{217}}{-6}
$