5/8x+3/4x=11

Solution for 5/8x+3/4x=11 equation:

5/8x+3/4x=11

We move all terms to the left:

5/8x+3/4x-(11)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


20x/32x^2+24x/32x^2-11=0

We multiply all the terms by the denominator


20x+24x-11*32x^2=0

We add all the numbers together, and all the variables

44x-11*32x^2=0

Wy multiply elements

-352x^2+44x=0

a = -352; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-352)·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*-352}=\frac{-88}{-704}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-352}=\frac{0}{-704}
=0
$