24=2x^2+4x-6

Solution for 24=2x^2+4x-6 equation:

24=2x^2+4x-6

We move all terms to the left:

24-(2x^2+4x-6)=0

We get rid of parentheses

-2x^2-4x+6+24=0

We add all the numbers together, and all the variables

-2x^2-4x+30=0

a = -2; b = -4; c = +30;
Δ = b2-4ac
Δ = -42-4·(-2)·30
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-2}=\frac{20}{-4}
=-5
$