X^2-7x+12.25=11

Solution for X^2-7x+12.25=11 equation:

X^2-7X+12.25=11

We move all terms to the left:

X^2-7X+12.25-(11)=0

We add all the numbers together, and all the variables

X^2-7X+1.25=0

a = 1; b = -7; c = +1.25;
Δ = b2-4ac
Δ = -72-4·1·1.25
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-2\sqrt{11}}{2*1}=\frac{7-2\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+2\sqrt{11}}{2*1}=\frac{7+2\sqrt{11}}{2}
$