x^2-30x=-224

Solution for x^2-30x=-224 equation:

x^2-30x=-224

We move all terms to the left:

x^2-30x-(-224)=0

We add all the numbers together, and all the variables

x^2-30x+224=0

a = 1; b = -30; c = +224;
Δ = b2-4ac
Δ = -302-4·1·224
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2}{2*1}=\frac{28}{2}
=14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2}{2*1}=\frac{32}{2}
=16
$