X^2-7x=23

Solution for X^2-7x=23 equation:

X^2-7X=23

We move all terms to the left:

X^2-7X-(23)=0

a = 1; b = -7; c = -23;
Δ = b2-4ac
Δ = -72-4·1·(-23)
Δ = 141
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{-(-7)-\sqrt{141}}{2*1}=\frac{7-\sqrt{141}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{141}}{2*1}=\frac{7+\sqrt{141}}{2}
$