6=2x^2+4x-3

Solution for 6=2x^2+4x-3 equation:

6=2x^2+4x-3

We move all terms to the left:

6-(2x^2+4x-3)=0

We get rid of parentheses

-2x^2-4x+3+6=0

We add all the numbers together, and all the variables

-2x^2-4x+9=0

a = -2; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-2)·9
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*-2}=\frac{4-2\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*-2}=\frac{4+2\sqrt{22}}{-4}
$