4x^2=-8x+221

Solution for 4x^2=-8x+221 equation:

4x^2=-8x+221

We move all terms to the left:

4x^2-(-8x+221)=0

We get rid of parentheses

4x^2+8x-221=0

a = 4; b = 8; c = -221;
Δ = b2-4ac
Δ = 82-4·4·(-221)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-60}{2*4}=\frac{-68}{8}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+60}{2*4}=\frac{52}{8}
=6+1/2
$