1/2x+x=225

Solution for 1/2x+x=225 equation:

1/2x+x=225

We move all terms to the left:

1/2x+x-(225)=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+1/2x-225=0

We multiply all the terms by the denominator


x*2x-225*2x+1=0

Wy multiply elements

2x^2-450x+1=0

a = 2; b = -450; c = +1;
Δ = b2-4ac
Δ = -4502-4·2·1
Δ = 202492
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:

$\sqrt{\Delta}=\sqrt{202492}=\sqrt{4*50623}=\sqrt{4}*\sqrt{50623}=2\sqrt{50623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50623}}{2*2}=\frac{450-2\sqrt{50623}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50623}}{2*2}=\frac{450+2\sqrt{50623}}{4}
$