6x2+3x-2=-2x2-5x+8

Solution for 6x2+3x-2=-2x2-5x+8 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2+8x-10=0

a = 8; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·8·(-10)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*8}=\frac{-8-8\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*8}=\frac{-8+8\sqrt{6}}{16}
$