x^2+6x=11.25

Solution for x^2+6x=11.25 equation:

x^2+6x=11.25

We move all terms to the left:

x^2+6x-(11.25)=0

We add all the numbers together, and all the variables

x^2+6x-11.25=0

a = 1; b = 6; c = -11.25;
Δ = b2-4ac
Δ = 62-4·1·(-11.25)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-9}{2*1}=\frac{-15}{2}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+9}{2*1}=\frac{3}{2}
=1+1/2
$