31/4x+11/8x=35

Solution for 31/4x+11/8x=35 equation:

31/4x+11/8x=35

We move all terms to the left:

31/4x+11/8x-(35)=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


248x/32x^2+44x/32x^2-35=0

We multiply all the terms by the denominator


248x+44x-35*32x^2=0

We add all the numbers together, and all the variables

292x-35*32x^2=0

Wy multiply elements

-1120x^2+292x=0

a = -1120; b = 292; c = 0;
Δ = b2-4ac
Δ = 2922-4·(-1120)·0
Δ = 85264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{85264}=292$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(292)-292}{2*-1120}=\frac{-584}{-2240}
=73/280
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(292)+292}{2*-1120}=\frac{0}{-2240}
=0
$