x/2x+x=90

Solution for x/2x+x=90 equation:

x/2x+x=90

We move all terms to the left:

x/2x+x-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+x/2x-90=0

We multiply all the terms by the denominator


x*2x+x-90*2x=0

We add all the numbers together, and all the variables

x+x*2x-90*2x=0

Wy multiply elements

2x^2+x-180x=0

We add all the numbers together, and all the variables

2x^2-179x=0

a = 2; b = -179; c = 0;
Δ = b2-4ac
Δ = -1792-4·2·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-179}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+179}{2*2}=\frac{358}{4}
=89+1/2
$