1/5(25x+10)-5=-1/4(16x-28)

Solution for 1/5(25x+10)-5=-1/4(16x-28) equation:

1/5(25x+10)-5=-1/4(16x-28)

We move all terms to the left:

1/5(25x+10)-5-(-1/4(16x-28))=0


Domain of the equation: 5(25x+10)!=0

x∈R



Domain of the equation: 4(16x-28))!=0

x∈R


We calculate fractions


(4x1/(5(25x+10)*4(16x-28)))+(-(-5x2)/(5(25x+10)*4(16x-28)))-5=0


We calculate terms in parentheses: +(4x1/(5(25x+10)*4(16x-28))), so:

4x1/(5(25x+10)*4(16x-28))

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+10)*4(16x-28))), so:

-(-5x2)/(5(25x+10)*4(16x-28))

We add all the numbers together, and all the variables

-(-5x^2)/(5(25x+10)*4(16x-28))

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-5=0

a = 5; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·5·(-5)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{29}}{2*5}=\frac{-4-2\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{29}}{2*5}=\frac{-4+2\sqrt{29}}{10}
$