3/5(x)=10/9x+3

Solution for 3/5(x)=10/9x+3 equation:

3/5(x)=10/9x+3

We move all terms to the left:

3/5(x)-(10/9x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 9x+3)!=0

x∈R


We get rid of parentheses

3/5x-10/9x-3=0

We calculate fractions


27x/45x^2+(-50x)/45x^2-3=0

We multiply all the terms by the denominator


27x+(-50x)-3*45x^2=0

Wy multiply elements

-135x^2+27x+(-50x)=0

We get rid of parentheses

-135x^2+27x-50x=0

We add all the numbers together, and all the variables

-135x^2-23x=0

a = -135; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-135)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-135}=\frac{0}{-270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-135}=\frac{46}{-270}
=-23/135
$