x2+15x=37.5

Solution for x2+15x=37.5 equation:

x2+15x=37.5

We move all terms to the left:

x2+15x-(37.5)=0

We add all the numbers together, and all the variables

x^2+15x-37.5=0

a = 1; b = 15; c = -37.5;
Δ = b2-4ac
Δ = 152-4·1·(-37.5)
Δ = 375
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{375}=\sqrt{25*15}=\sqrt{25}*\sqrt{15}=5\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{15}}{2*1}=\frac{-15-5\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{15}}{2*1}=\frac{-15+5\sqrt{15}}{2}
$