1/2(18x+16)-6=-3/5(20x-35)

Solution for 1/2(18x+16)-6=-3/5(20x-35) equation:

1/2(18x+16)-6=-3/5(20x-35)

We move all terms to the left:

1/2(18x+16)-6-(-3/5(20x-35))=0


Domain of the equation: 2(18x+16)!=0

x∈R



Domain of the equation: 5(20x-35))!=0

x∈R


We calculate fractions


(5x2/(2(18x+16)*5(20x-35)))+(-(-6x1)/(2(18x+16)*5(20x-35)))-6=0


We calculate terms in parentheses: +(5x2/(2(18x+16)*5(20x-35))), so:

5x2/(2(18x+16)*5(20x-35))

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: +(-(-6x1)/(2(18x+16)*5(20x-35))), so:

-(-6x1)/(2(18x+16)*5(20x-35))

We add all the numbers together, and all the variables

-(-6x)/(2(18x+16)*5(20x-35))

We multiply all the terms by the denominator


-(-6x)

We get rid of parentheses

6x

Back to the equation:

+(6x)


a = 5; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·5·(-6)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*5}=\frac{-6-2\sqrt{39}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*5}=\frac{-6+2\sqrt{39}}{10}
$