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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3x^2+5x-(-1x-8)-3=0

We get rid of parentheses

-3x^2+5x+1x+8-3=0

We add all the numbers together, and all the variables

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

a = -3; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-3)·5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*-3}=\frac{-6-4\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*-3}=\frac{-6+4\sqrt{6}}{-6}
$