7x^2+4x=4

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

7x^2+4x=4

We move all terms to the left:

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

a = 7; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·7·(-4)
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*7}=\frac{-4-8\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{2}}{2*7}=\frac{-4+8\sqrt{2}}{14}
$