x^2+5x+6.25=40

Solution for x^2+5x+6.25=40 equation:

x^2+5x+6.25=40

We move all terms to the left:

x^2+5x+6.25-(40)=0

We add all the numbers together, and all the variables

x^2+5x-33.75=0

a = 1; b = 5; c = -33.75;
Δ = b2-4ac
Δ = 52-4·1·(-33.75)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-4\sqrt{10}}{2*1}=\frac{-5-4\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+4\sqrt{10}}{2*1}=\frac{-5+4\sqrt{10}}{2}
$