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

Solution for x^2+4x+50-2x^2=0 equation:

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

We add all the numbers together, and all the variables

-1x^2+4x+50=0

a = -1; b = 4; c = +50;
Δ = b2-4ac
Δ = 42-4·(-1)·50
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{6}}{2*-1}=\frac{-4-6\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{6}}{2*-1}=\frac{-4+6\sqrt{6}}{-2}
$