551=4x^2+60x+200

Solution for 551=4x^2+60x+200 equation:

551=4x^2+60x+200

We move all terms to the left:

551-(4x^2+60x+200)=0

We get rid of parentheses

-4x^2-60x-200+551=0

We add all the numbers together, and all the variables

-4x^2-60x+351=0

a = -4; b = -60; c = +351;
Δ = b2-4ac
Δ = -602-4·(-4)·351
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-96}{2*-4}=\frac{-36}{-8}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+96}{2*-4}=\frac{156}{-8}
=-19+1/2
$