4/6X-5=5/2x+10

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

4/6X-5=5/2X+10

We move all terms to the left:

4/6X-5-(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-10-5=0

We calculate fractions


8X/12X^2+(-30X)/12X^2-10-5=0

We add all the numbers together, and all the variables

8X/12X^2+(-30X)/12X^2-15=0

We multiply all the terms by the denominator


8X+(-30X)-15*12X^2=0

Wy multiply elements

-180X^2+8X+(-30X)=0

We get rid of parentheses

-180X^2+8X-30X=0

We add all the numbers together, and all the variables

-180X^2-22X=0

a = -180; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-180)·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*-180}=\frac{0}{-360}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-180}=\frac{44}{-360}
=-11/90
$