4/6x=5/2x+10

Solution for 4/6x=5/2x+10 equation:

4/6x=5/2x+10

We move all terms to the left:

4/6x-(5/2x+10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+10)!=0

x∈R


We get rid of parentheses

4/6x-5/2x-10=0

We calculate fractions


8x/12x^2+(-30x)/12x^2-10=0

We multiply all the terms by the denominator


8x+(-30x)-10*12x^2=0

Wy multiply elements

-120x^2+8x+(-30x)=0

We get rid of parentheses

-120x^2+8x-30x=0

We add all the numbers together, and all the variables

-120x^2-22x=0

a = -120; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-120)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-120}=\frac{44}{-240}
=-11/60
$