6x(x-5)=23

Solution for 6x(x-5)=23 equation:

6x(x-5)=23

We move all terms to the left:

6x(x-5)-(23)=0

We multiply parentheses

6x^2-30x-23=0

a = 6; b = -30; c = -23;
Δ = b2-4ac
Δ = -302-4·6·(-23)
Δ = 1452
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:

$\sqrt{\Delta}=\sqrt{1452}=\sqrt{484*3}=\sqrt{484}*\sqrt{3}=22\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-22\sqrt{3}}{2*6}=\frac{30-22\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+22\sqrt{3}}{2*6}=\frac{30+22\sqrt{3}}{12}
$