6=4x^2+2x-5

Solution for 6=4x^2+2x-5 equation:

6=4x^2+2x-5

We move all terms to the left:

6-(4x^2+2x-5)=0

We get rid of parentheses

-4x^2-2x+5+6=0

We add all the numbers together, and all the variables

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

a = -4; b = -2; c = +11;
Δ = b2-4ac
Δ = -22-4·(-4)·11
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{5}}{2*-4}=\frac{2-6\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{5}}{2*-4}=\frac{2+6\sqrt{5}}{-8}
$