42/3x-4/5=7/15x

Solution for 42/3x-4/5=7/15x equation:

42/3x-4/5=7/15x

We move all terms to the left:

42/3x-4/5-(7/15x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

42/3x-(+7/15x)-4/5=0

We get rid of parentheses

42/3x-7/15x-4/5=0

We calculate fractions


(-180x^2)/1125x^2+15750x/1125x^2+(-525x)/1125x^2=0

We multiply all the terms by the denominator


(-180x^2)+15750x+(-525x)=0

We get rid of parentheses

-180x^2+15750x-525x=0

We add all the numbers together, and all the variables

-180x^2+15225x=0

a = -180; b = 15225; c = 0;
Δ = b2-4ac
Δ = 152252-4·(-180)·0
Δ = 231800625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{231800625}=15225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15225)-15225}{2*-180}=\frac{-30450}{-360}
=84+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15225)+15225}{2*-180}=\frac{0}{-360}
=0
$