X2+45x=-200

Solution for X2+45x=-200 equation:

X2+45X=-200

We move all terms to the left:

X2+45X-(-200)=0

We add all the numbers together, and all the variables

X^2+45X+200=0

a = 1; b = 45; c = +200;
Δ = b2-4ac
Δ = 452-4·1·200
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-35}{2*1}=\frac{-80}{2}
=-40
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+35}{2*1}=\frac{-10}{2}
=-5
$