X2-3x=23

Solution for X2-3x=23 equation:

X2-3X=23

We move all terms to the left:

X2-3X-(23)=0

We add all the numbers together, and all the variables

X^2-3X-23=0

a = 1; b = -3; c = -23;
Δ = b2-4ac
Δ = -32-4·1·(-23)
Δ = 101
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{-(-3)-\sqrt{101}}{2*1}=\frac{3-\sqrt{101}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{101}}{2*1}=\frac{3+\sqrt{101}}{2}
$