5/3x+1/2=4/7x+8

Solution for 5/3x+1/2=4/7x+8 equation:

5/3x+1/2=4/7x+8

We move all terms to the left:

5/3x+1/2-(4/7x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x+8)!=0

x∈R


We get rid of parentheses

5/3x-4/7x-8+1/2=0

We calculate fractions


147x^2/84x^2+140x/84x^2+(-48x)/84x^2-8=0

We multiply all the terms by the denominator


147x^2+140x+(-48x)-8*84x^2=0

Wy multiply elements

147x^2-672x^2+140x+(-48x)=0

We get rid of parentheses

147x^2-672x^2+140x-48x=0

We add all the numbers together, and all the variables

-525x^2+92x=0

a = -525; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-525)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-525}=\frac{-184}{-1050}
=92/525
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-525}=\frac{0}{-1050}
=0
$