(1/2)2x-8=15

Solution for (1/2)2x-8=15 equation:

(1/2)2x-8=15

We move all terms to the left:

(1/2)2x-8-(15)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)2x-8-15=0

We add all the numbers together, and all the variables

(+1/2)2x-23=0

We multiply parentheses

2x^2-23=0

a = 2; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·2·(-23)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{46}}{2*2}=\frac{0-2\sqrt{46}}{4}
=-\frac{2\sqrt{46}}{4}
=-\frac{\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{46}}{2*2}=\frac{0+2\sqrt{46}}{4}
=\frac{2\sqrt{46}}{4}
=\frac{\sqrt{46}}{2}
$