2/5(25x+15)-17=-1/2(16x-14)

Solution for 2/5(25x+15)-17=-1/2(16x-14) equation:

2/5(25x+15)-17=-1/2(16x-14)

We move all terms to the left:

2/5(25x+15)-17-(-1/2(16x-14))=0


Domain of the equation: 5(25x+15)!=0

x∈R



Domain of the equation: 2(16x-14))!=0

x∈R


We calculate fractions


(4x1/(5(25x+15)*2(16x-14)))+(-(-5x2)/(5(25x+15)*2(16x-14)))-17=0


We calculate terms in parentheses: +(4x1/(5(25x+15)*2(16x-14))), so:

4x1/(5(25x+15)*2(16x-14))

We multiply all the terms by the denominator


4x1

We add all the numbers together, and all the variables

4x

Back to the equation:

+(4x)



We calculate terms in parentheses: +(-(-5x2)/(5(25x+15)*2(16x-14))), so:

-(-5x2)/(5(25x+15)*2(16x-14))

We add all the numbers together, and all the variables

-(-5x^2)/(5(25x+15)*2(16x-14))

We multiply all the terms by the denominator


-(-5x^2)

We get rid of parentheses

5x^2

Back to the equation:

+(5x^2)


determiningTheFunctionDomain
5x^2+4x-17=0

a = 5; b = 4; c = -17;
Δ = b2-4ac
Δ = 42-4·5·(-17)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{89}}{2*5}=\frac{-4-2\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{89}}{2*5}=\frac{-4+2\sqrt{89}}{10}
$