2/4x-15=5/7x-16

Solution for 2/4x-15=5/7x-16 equation:

2/4x-15=5/7x-16

We move all terms to the left:

2/4x-15-(5/7x-16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x-16)!=0

x∈R


We get rid of parentheses

2/4x-5/7x+16-15=0

We calculate fractions


14x/28x^2+(-20x)/28x^2+16-15=0

We add all the numbers together, and all the variables

14x/28x^2+(-20x)/28x^2+1=0

We multiply all the terms by the denominator


14x+(-20x)+1*28x^2=0

Wy multiply elements

28x^2+14x+(-20x)=0

We get rid of parentheses

28x^2+14x-20x=0

We add all the numbers together, and all the variables

28x^2-6x=0

a = 28; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·28·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*28}=\frac{12}{56}
=3/14
$