-3x^2-5x-1=8x^2+2x-9

Solution for -3x^2-5x-1=8x^2+2x-9 equation:

-3x^2-5x-1=8x^2+2x-9

We move all terms to the left:

-3x^2-5x-1-(8x^2+2x-9)=0

We get rid of parentheses

-3x^2-8x^2-5x-2x+9-1=0

We add all the numbers together, and all the variables

-11x^2-7x+8=0

a = -11; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-11)·8
Δ = 401
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{-(-7)-\sqrt{401}}{2*-11}=\frac{7-\sqrt{401}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{401}}{2*-11}=\frac{7+\sqrt{401}}{-22}
$