x^2+4x=206.25

Solution for x^2+4x=206.25 equation:

x^2+4x=206.25

We move all terms to the left:

x^2+4x-(206.25)=0

We add all the numbers together, and all the variables

x^2+4x-206.25=0

a = 1; b = 4; c = -206.25;
Δ = b2-4ac
Δ = 42-4·1·(-206.25)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-29}{2*1}=\frac{-33}{2}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+29}{2*1}=\frac{25}{2}
=12+1/2
$