8/7x+3/4x=53/28

Solution for 8/7x+3/4x=53/28 equation:

8/7x+3/4x=53/28

We move all terms to the left:

8/7x+3/4x-(53/28)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8/7x+3/4x-(+53/28)=0

We get rid of parentheses

8/7x+3/4x-53/28=0

We calculate fractions


(-5936x^2)/1568x^2+1792x/1568x^2+1176x/1568x^2=0

We multiply all the terms by the denominator


(-5936x^2)+1792x+1176x=0

We add all the numbers together, and all the variables

(-5936x^2)+2968x=0

We get rid of parentheses

-5936x^2+2968x=0

a = -5936; b = 2968; c = 0;
Δ = b2-4ac
Δ = 29682-4·(-5936)·0
Δ = 8809024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8809024}=2968$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2968)-2968}{2*-5936}=\frac{-5936}{-11872}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2968)+2968}{2*-5936}=\frac{0}{-11872}
=0
$