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}
$