4x^2+2x=83

Solution for 4x^2+2x=83 equation:

4x^2+2x=83

We move all terms to the left:

4x^2+2x-(83)=0

a = 4; b = 2; c = -83;
Δ = b2-4ac
Δ = 22-4·4·(-83)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{37}}{2*4}=\frac{-2-6\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{37}}{2*4}=\frac{-2+6\sqrt{37}}{8}
$