X=-x^2+3x+28

Solution for X=-x^2+3x+28 equation:

X=-X^2+3X+28

We move all terms to the left:

X-(-X^2+3X+28)=0

We get rid of parentheses

X^2-3X+X-28=0

We add all the numbers together, and all the variables

X^2-2X-28=0

a = 1; b = -2; c = -28;
Δ = b2-4ac
Δ = -22-4·1·(-28)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*1}=\frac{2-2\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*1}=\frac{2+2\sqrt{29}}{2}
$