3/5x-7=1/4x+8

Solution for 3/5x-7=1/4x+8 equation:

3/5x-7=1/4x+8

We move all terms to the left:

3/5x-7-(1/4x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/5x-1/4x-8-7=0

We calculate fractions


12x/20x^2+(-5x)/20x^2-8-7=0

We add all the numbers together, and all the variables

12x/20x^2+(-5x)/20x^2-15=0

We multiply all the terms by the denominator


12x+(-5x)-15*20x^2=0

Wy multiply elements

-300x^2+12x+(-5x)=0

We get rid of parentheses

-300x^2+12x-5x=0

We add all the numbers together, and all the variables

-300x^2+7x=0

a = -300; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-300)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-300}=\frac{-14}{-600}
=7/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-300}=\frac{0}{-600}
=0
$