23x+14=11/6x-13

Solution for 23x+14=11/6x-13 equation:

23x+14=11/6x-13

We move all terms to the left:

23x+14-(11/6x-13)=0


Domain of the equation: 6x-13)!=0

x∈R


We get rid of parentheses

23x-11/6x+13+14=0

We multiply all the terms by the denominator


23x*6x+13*6x+14*6x-11=0

Wy multiply elements

138x^2+78x+84x-11=0

We add all the numbers together, and all the variables

138x^2+162x-11=0

a = 138; b = 162; c = -11;
Δ = b2-4ac
Δ = 1622-4·138·(-11)
Δ = 32316
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:

$\sqrt{\Delta}=\sqrt{32316}=\sqrt{4*8079}=\sqrt{4}*\sqrt{8079}=2\sqrt{8079}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{8079}}{2*138}=\frac{-162-2\sqrt{8079}}{276}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{8079}}{2*138}=\frac{-162+2\sqrt{8079}}{276}
$