37x+(x^2)=-100

Solution for 37x+(x^2)=-100 equation:

37x+(x^2)=-100

We move all terms to the left:

37x+(x^2)-(-100)=0

determiningTheFunctionDomain
x^2+37x-(-100)=0

We add all the numbers together, and all the variables

x^2+37x+100=0

a = 1; b = 37; c = +100;
Δ = b2-4ac
Δ = 372-4·1·100
Δ = 969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{969}}{2*1}=\frac{-37-\sqrt{969}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{969}}{2*1}=\frac{-37+\sqrt{969}}{2}
$