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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

11x-(6x^2-3)-2=0

We get rid of parentheses

-6x^2+11x+3-2=0

We add all the numbers together, and all the variables

-6x^2+11x+1=0

a = -6; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-6)·1
Δ = 145
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{145}}{2*-6}=\frac{-11-\sqrt{145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{145}}{2*-6}=\frac{-11+\sqrt{145}}{-12}
$