x+12=1/23x-8

Solution for x+12=1/23x-8 equation:

x+12=1/23x-8

We move all terms to the left:

x+12-(1/23x-8)=0


Domain of the equation: 23x-8)!=0

x∈R


We get rid of parentheses

x-1/23x+8+12=0

We multiply all the terms by the denominator


x*23x+8*23x+12*23x-1=0

Wy multiply elements

23x^2+184x+276x-1=0

We add all the numbers together, and all the variables

23x^2+460x-1=0

a = 23; b = 460; c = -1;
Δ = b2-4ac
Δ = 4602-4·23·(-1)
Δ = 211692
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:

$\sqrt{\Delta}=\sqrt{211692}=\sqrt{4*52923}=\sqrt{4}*\sqrt{52923}=2\sqrt{52923}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(460)-2\sqrt{52923}}{2*23}=\frac{-460-2\sqrt{52923}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(460)+2\sqrt{52923}}{2*23}=\frac{-460+2\sqrt{52923}}{46}
$