3(x+5)6x=23

Solution for 3(x+5)6x=23 equation:

3(x+5)6x=23

We move all terms to the left:

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

We multiply parentheses

18x^2+90x-23=0

a = 18; b = 90; c = -23;
Δ = b2-4ac
Δ = 902-4·18·(-23)
Δ = 9756
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:

$\sqrt{\Delta}=\sqrt{9756}=\sqrt{36*271}=\sqrt{36}*\sqrt{271}=6\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{271}}{2*18}=\frac{-90-6\sqrt{271}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{271}}{2*18}=\frac{-90+6\sqrt{271}}{36}
$