5/4x+7/8x=48/12

Solution for 5/4x+7/8x=48/12 equation:

5/4x+7/8x=48/12

We move all terms to the left:

5/4x+7/8x-(48/12)=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

5/4x+7/8x-4=0

We calculate fractions


40x/32x^2+28x/32x^2-4=0

We multiply all the terms by the denominator


40x+28x-4*32x^2=0

We add all the numbers together, and all the variables

68x-4*32x^2=0

Wy multiply elements

-128x^2+68x=0

a = -128; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-128)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-128}=\frac{-136}{-256}
=17/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-128}=\frac{0}{-256}
=0
$