1/4x+3/2x=22

Solution for 1/4x+3/2x=22 equation:

1/4x+3/2x=22

We move all terms to the left:

1/4x+3/2x-(22)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


2x/8x^2+12x/8x^2-22=0

We multiply all the terms by the denominator


2x+12x-22*8x^2=0

We add all the numbers together, and all the variables

14x-22*8x^2=0

Wy multiply elements

-176x^2+14x=0

a = -176; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-176)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-176}=\frac{-28}{-352}
=7/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-176}=\frac{0}{-352}
=0
$