1/3x+2=7/8x-3

Solution for 1/3x+2=7/8x-3 equation:

1/3x+2=7/8x-3

We move all terms to the left:

1/3x+2-(7/8x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 8x-3)!=0

x∈R


We get rid of parentheses

1/3x-7/8x+3+2=0

We calculate fractions


8x/24x^2+(-21x)/24x^2+3+2=0

We add all the numbers together, and all the variables

8x/24x^2+(-21x)/24x^2+5=0

We multiply all the terms by the denominator


8x+(-21x)+5*24x^2=0

Wy multiply elements

120x^2+8x+(-21x)=0

We get rid of parentheses

120x^2+8x-21x=0

We add all the numbers together, and all the variables

120x^2-13x=0

a = 120; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·120·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*120}=\frac{0}{240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*120}=\frac{26}{240}
=13/120
$