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

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

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

We move all terms to the left:

1/2x+271/2x+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


We calculate fractions


(1084x+1)/8x^2+6x/8x^2-90=0

We multiply all the terms by the denominator


(1084x+1)+6x-90*8x^2=0

We add all the numbers together, and all the variables

6x+(1084x+1)-90*8x^2=0

Wy multiply elements

-720x^2+6x+(1084x+1)=0

We get rid of parentheses

-720x^2+6x+1084x+1=0

We add all the numbers together, and all the variables

-720x^2+1090x+1=0

a = -720; b = 1090; c = +1;
Δ = b2-4ac
Δ = 10902-4·(-720)·1
Δ = 1190980
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1190980}=\sqrt{4*297745}=\sqrt{4}*\sqrt{297745}=2\sqrt{297745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1090)-2\sqrt{297745}}{2*-720}=\frac{-1090-2\sqrt{297745}}{-1440}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1090)+2\sqrt{297745}}{2*-720}=\frac{-1090+2\sqrt{297745}}{-1440}
$