(x-7)x=23

Solution for (x-7)x=23 equation:

(x-7)x=23

We move all terms to the left:

(x-7)x-(23)=0

We multiply parentheses

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}
$