5/6x-3=5/8x+10

Solution for 5/6x-3=5/8x+10 equation:

5/6x-3=5/8x+10

We move all terms to the left:

5/6x-3-(5/8x+10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x+10)!=0

x∈R


We get rid of parentheses

5/6x-5/8x-10-3=0

We calculate fractions


40x/48x^2+(-30x)/48x^2-10-3=0

We add all the numbers together, and all the variables

40x/48x^2+(-30x)/48x^2-13=0

We multiply all the terms by the denominator


40x+(-30x)-13*48x^2=0

Wy multiply elements

-624x^2+40x+(-30x)=0

We get rid of parentheses

-624x^2+40x-30x=0

We add all the numbers together, and all the variables

-624x^2+10x=0

a = -624; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-624)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-624}=\frac{-20}{-1248}
=5/312
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-624}=\frac{0}{-1248}
=0
$