X^2=2x+10.5

Solution for X^2=2x+10.5 equation:

X^2=2X+10.5

We move all terms to the left:

X^2-(2X+10.5)=0

We get rid of parentheses

X^2-2X-10.5=0

a = 1; b = -2; c = -10.5;
Δ = b2-4ac
Δ = -22-4·1·(-10.5)
Δ = 46
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{-(-2)-\sqrt{46}}{2*1}=\frac{2-\sqrt{46}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{46}}{2*1}=\frac{2+\sqrt{46}}{2}
$