x^2-7x=-7.75

Solution for x^2-7x=-7.75 equation:

x^2-7x=-7.75

We move all terms to the left:

x^2-7x-(-7.75)=0

We add all the numbers together, and all the variables

x^2-7x+7.75=0

a = 1; b = -7; c = +7.75;
Δ = b2-4ac
Δ = -72-4·1·7.75
Δ = 18
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:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{2}}{2*1}=\frac{7-3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{2}}{2*1}=\frac{7+3\sqrt{2}}{2}
$