x+1/2x=45

Solution for x+1/2x=45 equation:

x+1/2x=45

We move all terms to the left:

x+1/2x-(45)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-45*2x+1=0

Wy multiply elements

2x^2-90x+1=0

a = 2; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·2·1
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-34\sqrt{7}}{2*2}=\frac{90-34\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+34\sqrt{7}}{2*2}=\frac{90+34\sqrt{7}}{4}
$