3/4x+7/8x=28/12

Solution for 3/4x+7/8x=28/12 equation:

3/4x+7/8x=28/12

We move all terms to the left:

3/4x+7/8x-(28/12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+7/8x-(+28/12)=0

We get rid of parentheses

3/4x+7/8x-28/12=0

We calculate fractions


(-7168x^2)/384x^2+288x/384x^2+336x/384x^2=0

We multiply all the terms by the denominator


(-7168x^2)+288x+336x=0

We add all the numbers together, and all the variables

(-7168x^2)+624x=0

We get rid of parentheses

-7168x^2+624x=0

a = -7168; b = 624; c = 0;
Δ = b2-4ac
Δ = 6242-4·(-7168)·0
Δ = 389376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{389376}=624$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(624)-624}{2*-7168}=\frac{-1248}{-14336}
=39/448
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(624)+624}{2*-7168}=\frac{0}{-14336}
=0
$