x+(1)/(2)x=38

Solution for x+(1)/(2)x=38 equation:

x+(1)/(2)x=38

We move all terms to the left:

x+(1)/(2)x-(38)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-38*2x+1=0

Wy multiply elements

2x^2-76x+1=0

a = 2; b = -76; c = +1;
Δ = b2-4ac
Δ = -762-4·2·1
Δ = 5768
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:

$\sqrt{\Delta}=\sqrt{5768}=\sqrt{4*1442}=\sqrt{4}*\sqrt{1442}=2\sqrt{1442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1442}}{2*2}=\frac{76-2\sqrt{1442}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1442}}{2*2}=\frac{76+2\sqrt{1442}}{4}
$