1/2x+271/2+3/4x=90

Solution for 1/2x+271/2+3/4x=90 equation:

1/2x+271/2+3/4x=90

We move all terms to the left:

1/2x+271/2+3/4x-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
1/2x+3/4x-90+271/2=0

We calculate fractions


4x/32x^2+24x/32x^2+1084x/32x^2-90=0

We multiply all the terms by the denominator


4x+24x+1084x-90*32x^2=0

We add all the numbers together, and all the variables

1112x-90*32x^2=0

Wy multiply elements

-2880x^2+1112x=0

a = -2880; b = 1112; c = 0;
Δ = b2-4ac
Δ = 11122-4·(-2880)·0
Δ = 1236544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1236544}=1112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1112)-1112}{2*-2880}=\frac{-2224}{-5760}
=139/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1112)+1112}{2*-2880}=\frac{0}{-5760}
=0
$