x^2+21.75x=-1.75

Solution for x^2+21.75x=-1.75 equation:

x^2+21.75x=-1.75

We move all terms to the left:

x^2+21.75x-(-1.75)=0

We add all the numbers together, and all the variables

x^2+21.75x+1.75=0

a = 1; b = 21.75; c = +1.75;
Δ = b2-4ac
Δ = 21.752-4·1·1.75
Δ = 466.0625
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{-(21.75)-\sqrt{466.0625}}{2*1}=\frac{-21.75-\sqrt{466.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21.75)+\sqrt{466.0625}}{2*1}=\frac{-21.75+\sqrt{466.0625}}{2}
$