2/5x-6=8-3/8x

Solution for 2/5x-6=8-3/8x equation:

2/5x-6=8-3/8x

We move all terms to the left:

2/5x-6-(8-3/8x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-3/8x+8)-6=0

We get rid of parentheses

2/5x+3/8x-8-6=0

We calculate fractions


16x/40x^2+15x/40x^2-8-6=0

We add all the numbers together, and all the variables

16x/40x^2+15x/40x^2-14=0

We multiply all the terms by the denominator


16x+15x-14*40x^2=0

We add all the numbers together, and all the variables

31x-14*40x^2=0

Wy multiply elements

-560x^2+31x=0

a = -560; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-560)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-560}=\frac{-62}{-1120}
=31/560
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-560}=\frac{0}{-1120}
=0
$