X/4x-10=6x-4

Solution for X/4x-10=6x-4 equation:

X/4X-10=6X-4

We move all terms to the left:

X/4X-10-(6X-4)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We get rid of parentheses

X/4X-6X+4-10=0

We multiply all the terms by the denominator


X-6X*4X+4*4X-10*4X=0

Wy multiply elements

-24X^2+X+16X-40X=0

We add all the numbers together, and all the variables

-24X^2-23X=0

a = -24; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-24)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-24}=\frac{0}{-48}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-24}=\frac{46}{-48}
=-23/24
$