x^2=7.75x+2

Solution for x^2=7.75x+2 equation:

x^2=7.75x+2

We move all terms to the left:

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

We get rid of parentheses

x^2-7.75x-2=0

a = 1; b = -7.75; c = -2;
Δ = b2-4ac
Δ = -7.752-4·1·(-2)
Δ = 68.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7.75)-\sqrt{68.0625}}{2*1}=\frac{7.75-\sqrt{68.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.75)+\sqrt{68.0625}}{2*1}=\frac{7.75+\sqrt{68.0625}}{2}
$