1/4(16x+24)=1/5(25x-35)

Solution for 1/4(16x+24)=1/5(25x-35) equation:

1/4(16x+24)=1/5(25x-35)

We move all terms to the left:

1/4(16x+24)-(1/5(25x-35))=0


Domain of the equation: 4(16x+24)!=0

x∈R



Domain of the equation: 5(25x-35))!=0

x∈R


We calculate fractions


(5x2/(4(16x+24)*5(25x-35)))+(-4x1/(4(16x+24)*5(25x-35)))=0


We calculate terms in parentheses: +(5x2/(4(16x+24)*5(25x-35))), so:

5x2/(4(16x+24)*5(25x-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: +(-4x1/(4(16x+24)*5(25x-35))), so:

-4x1/(4(16x+24)*5(25x-35))

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 get rid of parentheses

5x^2-4x=0

a = 5; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·5·0
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*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*5}=\frac{8}{10}
=4/5
$