1/3x+1/2=8/5x-10

Solution for 1/3x+1/2=8/5x-10 equation:

1/3x+1/2=8/5x-10

We move all terms to the left:

1/3x+1/2-(8/5x-10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

1/3x-8/5x+10+1/2=0

We calculate fractions


75x^2/60x^2+20x/60x^2+(-96x)/60x^2+10=0

We multiply all the terms by the denominator


75x^2+20x+(-96x)+10*60x^2=0

Wy multiply elements

75x^2+600x^2+20x+(-96x)=0

We get rid of parentheses

75x^2+600x^2+20x-96x=0

We add all the numbers together, and all the variables

675x^2-76x=0

a = 675; b = -76; c = 0;
Δ = b2-4ac
Δ = -762-4·675·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-76}{2*675}=\frac{0}{1350}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+76}{2*675}=\frac{152}{1350}
=76/675
$