1/2(10x+18)-20=1/3(24x-27)

Solution for 1/2(10x+18)-20=1/3(24x-27) equation:

1/2(10x+18)-20=1/3(24x-27)

We move all terms to the left:

1/2(10x+18)-20-(1/3(24x-27))=0


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

x∈R



Domain of the equation: 3(24x-27))!=0

x∈R


We calculate fractions


(3x2/(2(10x+18)*3(24x-27)))+(-2x1/(2(10x+18)*3(24x-27)))-20=0


We calculate terms in parentheses: +(3x2/(2(10x+18)*3(24x-27))), so:

3x2/(2(10x+18)*3(24x-27))

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 calculate terms in parentheses: +(-2x1/(2(10x+18)*3(24x-27))), so:

-2x1/(2(10x+18)*3(24x-27))

We multiply all the terms by the denominator


-2x1

We add all the numbers together, and all the variables

-2x

Back to the equation:

+(-2x)


We get rid of parentheses

3x^2-2x-20=0

a = 3; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·3·(-20)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*3}=\frac{2-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*3}=\frac{2+2\sqrt{61}}{6}
$