x^2+3x=7.5

Solution for x^2+3x=7.5 equation:

x^2+3x=7.5

We move all terms to the left:

x^2+3x-(7.5)=0

We add all the numbers together, and all the variables

x^2+3x-7.5=0

a = 1; b = 3; c = -7.5;
Δ = b2-4ac
Δ = 32-4·1·(-7.5)
Δ = 39
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{-(3)-\sqrt{39}}{2*1}=\frac{-3-\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{39}}{2*1}=\frac{-3+\sqrt{39}}{2}
$