6/8x-3=5x+3

Solution for 6/8x-3=5x+3 equation:

6/8x-3=5x+3

We move all terms to the left:

6/8x-3-(5x+3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

6/8x-5x-3-3=0

We multiply all the terms by the denominator


-5x*8x-3*8x-3*8x+6=0

Wy multiply elements

-40x^2-24x-24x+6=0

We add all the numbers together, and all the variables

-40x^2-48x+6=0

a = -40; b = -48; c = +6;
Δ = b2-4ac
Δ = -482-4·(-40)·6
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{51}}{2*-40}=\frac{48-8\sqrt{51}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{51}}{2*-40}=\frac{48+8\sqrt{51}}{-80}
$