X^2+3x+2.25=15

Solution for X^2+3x+2.25=15 equation:

X^2+3X+2.25=15

We move all terms to the left:

X^2+3X+2.25-(15)=0

We add all the numbers together, and all the variables

X^2+3X-12.75=0

a = 1; b = 3; c = -12.75;
Δ = b2-4ac
Δ = 32-4·1·(-12.75)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-2\sqrt{15}}{2*1}=\frac{-3-2\sqrt{15}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+2\sqrt{15}}{2*1}=\frac{-3+2\sqrt{15}}{2}
$