2x+1/2x+2(1+x)=90

Solution for 2x+1/2x+2(1+x)=90 equation:

2x+1/2x+2(1+x)=90

We move all terms to the left:

2x+1/2x+2(1+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

2x+1/2x+2(x+1)-90=0

We multiply parentheses

2x+1/2x+2x+2-90=0

We multiply all the terms by the denominator


2x*2x+2x*2x+2*2x-90*2x+1=0

Wy multiply elements

4x^2+4x^2+4x-180x+1=0

We add all the numbers together, and all the variables

8x^2-176x+1=0

a = 8; b = -176; c = +1;
Δ = b2-4ac
Δ = -1762-4·8·1
Δ = 30944
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:

$\sqrt{\Delta}=\sqrt{30944}=\sqrt{16*1934}=\sqrt{16}*\sqrt{1934}=4\sqrt{1934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-4\sqrt{1934}}{2*8}=\frac{176-4\sqrt{1934}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+4\sqrt{1934}}{2*8}=\frac{176+4\sqrt{1934}}{16}
$