4x^2-2x-7=4

Solution for 4x^2-2x-7=4 equation:

4x^2-2x-7=4

We move all terms to the left:

4x^2-2x-7-(4)=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}
$