50x+4x^2=223

Solution for 50x+4x^2=223 equation:

50x+4x^2=223

We move all terms to the left:

50x+4x^2-(223)=0

a = 4; b = 50; c = -223;
Δ = b2-4ac
Δ = 502-4·4·(-223)
Δ = 6068
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:

$\sqrt{\Delta}=\sqrt{6068}=\sqrt{4*1517}=\sqrt{4}*\sqrt{1517}=2\sqrt{1517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{1517}}{2*4}=\frac{-50-2\sqrt{1517}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{1517}}{2*4}=\frac{-50+2\sqrt{1517}}{8}
$