X=2x-15/6x+8

Solution for X=2x-15/6x+8 equation:

X=2X-15/6X+8

We move all terms to the left:

X-(2X-15/6X+8)=0


Domain of the equation: 6X+8)!=0

X∈R


We get rid of parentheses

X-2X+15/6X-8=0

We multiply all the terms by the denominator


X*6X-2X*6X-8*6X+15=0

Wy multiply elements

6X^2-12X^2-48X+15=0

We add all the numbers together, and all the variables

-6X^2-48X+15=0

a = -6; b = -48; c = +15;
Δ = b2-4ac
Δ = -482-4·(-6)·15
Δ = 2664
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:

$\sqrt{\Delta}=\sqrt{2664}=\sqrt{36*74}=\sqrt{36}*\sqrt{74}=6\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{74}}{2*-6}=\frac{48-6\sqrt{74}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{74}}{2*-6}=\frac{48+6\sqrt{74}}{-12}
$