6/5x+1/3=1/2x+8

Solution for 6/5x+1/3=1/2x+8 equation:

6/5x+1/3=1/2x+8

We move all terms to the left:

6/5x+1/3-(1/2x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

6/5x-1/2x-8+1/3=0

We calculate fractions


20x^2/90x^2+108x/90x^2+(-45x)/90x^2-8=0

We multiply all the terms by the denominator


20x^2+108x+(-45x)-8*90x^2=0

Wy multiply elements

20x^2-720x^2+108x+(-45x)=0

We get rid of parentheses

20x^2-720x^2+108x-45x=0

We add all the numbers together, and all the variables

-700x^2+63x=0

a = -700; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-700)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-700}=\frac{-126}{-1400}
=9/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-700}=\frac{0}{-1400}
=0
$