x^2+5x+6.25=7

Solution for x^2+5x+6.25=7 equation:

x^2+5x+6.25=7

We move all terms to the left:

x^2+5x+6.25-(7)=0

We add all the numbers together, and all the variables

x^2+5x-0.75=0

a = 1; b = 5; c = -0.75;
Δ = b2-4ac
Δ = 52-4·1·(-0.75)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-2\sqrt{7}}{2*1}=\frac{-5-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+2\sqrt{7}}{2*1}=\frac{-5+2\sqrt{7}}{2}
$