X/6x-3=4x+5

Solution for X/6x-3=4x+5 equation:

X/6X-3=4X+5

We move all terms to the left:

X/6X-3-(4X+5)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We get rid of parentheses

X/6X-4X-5-3=0

We multiply all the terms by the denominator


X-4X*6X-5*6X-3*6X=0

Wy multiply elements

-24X^2+X-30X-18X=0

We add all the numbers together, and all the variables

-24X^2-47X=0

a = -24; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·(-24)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*-24}=\frac{0}{-48}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*-24}=\frac{94}{-48}
=-1+23/24
$