-4/3x+57=3/5x-30

Solution for -4/3x+57=3/5x-30 equation:

-4/3x+57=3/5x-30

We move all terms to the left:

-4/3x+57-(3/5x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-30)!=0

x∈R


We get rid of parentheses

-4/3x-3/5x+30+57=0

We calculate fractions


(-20x)/15x^2+(-9x)/15x^2+30+57=0

We add all the numbers together, and all the variables

(-20x)/15x^2+(-9x)/15x^2+87=0

We multiply all the terms by the denominator


(-20x)+(-9x)+87*15x^2=0

Wy multiply elements

1305x^2+(-20x)+(-9x)=0

We get rid of parentheses

1305x^2-20x-9x=0

We add all the numbers together, and all the variables

1305x^2-29x=0

a = 1305; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·1305·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*1305}=\frac{0}{2610}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*1305}=\frac{58}{2610}
=1/45
$