4x^2=50+2x^

Solution for 4x^2=50+2x^ equation:

4x^2=50+2x^

We move all terms to the left:

4x^2-(50+2x^)=0

We get rid of parentheses

4x^2-2x^-50=0

We add all the numbers together, and all the variables

4x^2-2x-50=0

a = 4; b = -2; c = -50;
Δ = b2-4ac
Δ = -22-4·4·(-50)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{201}}{2*4}=\frac{2-2\sqrt{201}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{201}}{2*4}=\frac{2+2\sqrt{201}}{8}
$