4x^2+11x-6=x^2-2

Solution for 4x^2+11x-6=x^2-2 equation:

4x^2+11x-6=x^2-2

We move all terms to the left:

4x^2+11x-6-(x^2-2)=0

We get rid of parentheses

4x^2-x^2+11x+2-6=0

We add all the numbers together, and all the variables

3x^2+11x-4=0

a = 3; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·3·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*3}=\frac{2}{6}
=1/3
$