9=1/2x+x

Solution for 9=1/2x+x equation:

9=1/2x+x

We move all terms to the left:

9-(1/2x+x)=0


Domain of the equation: 2x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+1/2x)+9=0

We get rid of parentheses

-x-1/2x+9=0

We multiply all the terms by the denominator


-x*2x+9*2x-1=0

Wy multiply elements

-2x^2+18x-1=0

a = -2; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-2)·(-1)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{79}}{2*-2}=\frac{-18-2\sqrt{79}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{79}}{2*-2}=\frac{-18+2\sqrt{79}}{-4}
$