-1/3(27x-15)=1/2(10-18x)

Solution for -1/3(27x-15)=1/2(10-18x) equation:

-1/3(27x-15)=1/2(10-18x)

We move all terms to the left:

-1/3(27x-15)-(1/2(10-18x))=0


Domain of the equation: 3(27x-15)!=0

x∈R



Domain of the equation: 2(10-18x))!=0

x∈R


We add all the numbers together, and all the variables

-1/3(27x-15)-(1/2(-18x+10))=0

We calculate fractions


(-2x(-)/(3(27x-15)*2(-18x+10)))+(-3x2/(3(27x-15)*2(-18x+10)))=0


We calculate terms in parentheses: +(-2x(-)/(3(27x-15)*2(-18x+10))), so:

-2x(-)/(3(27x-15)*2(-18x+10))

We add all the numbers together, and all the variables

-2x0/(3(27x-15)*2(-18x+10))

We multiply all the terms by the denominator


-2x0

We add all the numbers together, and all the variables

-2x

Back to the equation:

+(-2x)



We calculate terms in parentheses: +(-3x2/(3(27x-15)*2(-18x+10))), so:

-3x2/(3(27x-15)*2(-18x+10))

We multiply all the terms by the denominator


-3x2

We add all the numbers together, and all the variables

-3x^2

Back to the equation:

+(-3x^2)


We get rid of parentheses

-3x^2-2x=0

a = -3; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-3)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-3}=\frac{4}{-6}
=-2/3
$