3/4x+5/8x=2

Solution for 3/4x+5/8x=2 equation:

3/4x+5/8x=2

We move all terms to the left:

3/4x+5/8x-(2)=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 calculate fractions


24x/32x^2+20x/32x^2-2=0

We multiply all the terms by the denominator


24x+20x-2*32x^2=0

We add all the numbers together, and all the variables

44x-2*32x^2=0

Wy multiply elements

-64x^2+44x=0

a = -64; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-64)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-64}=\frac{-88}{-128}
=11/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-64}=\frac{0}{-128}
=0
$