x^2+5x+6.25=49

Solution for x^2+5x+6.25=49 equation:

x^2+5x+6.25=49

We move all terms to the left:

x^2+5x+6.25-(49)=0

We add all the numbers together, and all the variables

x^2+5x-42.75=0

a = 1; b = 5; c = -42.75;
Δ = b2-4ac
Δ = 52-4·1·(-42.75)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-14}{2*1}=\frac{-19}{2}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+14}{2*1}=\frac{9}{2}
=4+1/2
$