X^2+7.5x=7.5

Solution for X^2+7.5x=7.5 equation:

X^2+7.5X=7.5

We move all terms to the left:

X^2+7.5X-(7.5)=0

We add all the numbers together, and all the variables

X^2+7.5X-7.5=0

a = 1; b = 7.5; c = -7.5;
Δ = b2-4ac
Δ = 7.52-4·1·(-7.5)
Δ = 86.25
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{-(7.5)-\sqrt{86.25}}{2*1}=\frac{-7.5-\sqrt{86.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{86.25}}{2*1}=\frac{-7.5+\sqrt{86.25}}{2}
$