1/3x+2=236/78x-3

Solution for 1/3x+2=236/78x-3 equation:

1/3x+2=236/78x-3

We move all terms to the left:

1/3x+2-(236/78x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 78x-3)!=0

x∈R


We get rid of parentheses

1/3x-236/78x+3+2=0

We calculate fractions


78x/234x^2+(-708x)/234x^2+3+2=0

We add all the numbers together, and all the variables

78x/234x^2+(-708x)/234x^2+5=0

We multiply all the terms by the denominator


78x+(-708x)+5*234x^2=0

Wy multiply elements

1170x^2+78x+(-708x)=0

We get rid of parentheses

1170x^2+78x-708x=0

We add all the numbers together, and all the variables

1170x^2-630x=0

a = 1170; b = -630; c = 0;
Δ = b2-4ac
Δ = -6302-4·1170·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-630}{2*1170}=\frac{0}{2340}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+630}{2*1170}=\frac{1260}{2340}
=7/13
$