1/5(25x-40)=3/4(16x+8)

Solution for 1/5(25x-40)=3/4(16x+8) equation:

1/5(25x-40)=3/4(16x+8)

We move all terms to the left:

1/5(25x-40)-(3/4(16x+8))=0


Domain of the equation: 5(25x-40)!=0

x∈R



Domain of the equation: 4(16x+8))!=0

x∈R


We calculate fractions


(4x1/(5(25x-40)*4(16x+8)))+(-15x2/(5(25x-40)*4(16x+8)))=0


We calculate terms in parentheses: +(4x1/(5(25x-40)*4(16x+8))), so:

4x1/(5(25x-40)*4(16x+8))

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: +(-15x2/(5(25x-40)*4(16x+8))), so:

-15x2/(5(25x-40)*4(16x+8))

We multiply all the terms by the denominator


-15x2

We add all the numbers together, and all the variables

-15x^2

Back to the equation:

+(-15x^2)


We get rid of parentheses

-15x^2+4x=0

a = -15; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-15)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-15}=\frac{-8}{-30}
=4/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-15}=\frac{0}{-30}
=0
$