12x(x+10)=23

Solution for 12x(x+10)=23 equation:

12x(x+10)=23

We move all terms to the left:

12x(x+10)-(23)=0

We multiply parentheses

12x^2+120x-23=0

a = 12; b = 120; c = -23;
Δ = b2-4ac
Δ = 1202-4·12·(-23)
Δ = 15504
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:

$\sqrt{\Delta}=\sqrt{15504}=\sqrt{16*969}=\sqrt{16}*\sqrt{969}=4\sqrt{969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{969}}{2*12}=\frac{-120-4\sqrt{969}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{969}}{2*12}=\frac{-120+4\sqrt{969}}{24}
$