4x^2-7=-4x

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

4x^2-7=-4x

We move all terms to the left:

4x^2-7-(-4x)=0

We get rid of parentheses

4x^2+4x-7=0

a = 4; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·4·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{2}}{2*4}=\frac{-4-8\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{2}}{2*4}=\frac{-4+8\sqrt{2}}{8}
$