1/2(12x+8)-10=-1/5(20x-15)

Solution for 1/2(12x+8)-10=-1/5(20x-15) equation:

1/2(12x+8)-10=-1/5(20x-15)

We move all terms to the left:

1/2(12x+8)-10-(-1/5(20x-15))=0


Domain of the equation: 2(12x+8)!=0

x∈R



Domain of the equation: 5(20x-15))!=0

x∈R


We calculate fractions


(5x2/(2(12x+8)*5(20x-15)))+(-(-2x1)/(2(12x+8)*5(20x-15)))-10=0


We calculate terms in parentheses: +(5x2/(2(12x+8)*5(20x-15))), so:

5x2/(2(12x+8)*5(20x-15))

We multiply all the terms by the denominator


5x2

We add all the numbers together, and all the variables

5x^2

Back to the equation:

+(5x^2)



We calculate terms in parentheses: +(-(-2x1)/(2(12x+8)*5(20x-15))), so:

-(-2x1)/(2(12x+8)*5(20x-15))

We add all the numbers together, and all the variables

-(-2x)/(2(12x+8)*5(20x-15))

We multiply all the terms by the denominator


-(-2x)

We get rid of parentheses

2x

Back to the equation:

+(2x)


a = 5; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·5·(-10)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{51}}{2*5}=\frac{-2-2\sqrt{51}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{51}}{2*5}=\frac{-2+2\sqrt{51}}{10}
$