(3/5)x=21/15-2x

Solution for (3/5)x=21/15-2x equation:

(3/5)x=21/15-2x

We move all terms to the left:

(3/5)x-(21/15-2x)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 15-2x)!=0

We move all terms containing x to the left, all other terms to the right

-2x)!=-15

x!=-15/1

x!=-15

x∈R


We add all the numbers together, and all the variables

(+3/5)x-(-2x+21/15)=0

We multiply parentheses

3x^2-(-2x+21/15)=0

We get rid of parentheses

3x^2+2x-21/15=0

We multiply all the terms by the denominator


3x^2*15+2x*15-21=0

Wy multiply elements

45x^2+30x-21=0

a = 45; b = 30; c = -21;
Δ = b2-4ac
Δ = 302-4·45·(-21)
Δ = 4680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4680}=\sqrt{36*130}=\sqrt{36}*\sqrt{130}=6\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{130}}{2*45}=\frac{-30-6\sqrt{130}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{130}}{2*45}=\frac{-30+6\sqrt{130}}{90}
$