X+x^2=15.75

Solution for X+x^2=15.75 equation:

X+X^2=15.75

We move all terms to the left:

X+X^2-(15.75)=0

We add all the numbers together, and all the variables

X^2+X-15.75=0

a = 1; b = 1; c = -15.75;
Δ = b2-4ac
Δ = 12-4·1·(-15.75)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-8}{2*1}=\frac{-9}{2}
=-4+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+8}{2*1}=\frac{7}{2}
=3+1/2
$