(1/2)15x=205

Solution for (1/2)15x=205 equation:

(1/2)15x=205

We move all terms to the left:

(1/2)15x-(205)=0


Domain of the equation: 2)15x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)15x-205=0

We multiply parentheses

15x^2-205=0

a = 15; b = 0; c = -205;
Δ = b2-4ac
Δ = 02-4·15·(-205)
Δ = 12300
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:

$\sqrt{\Delta}=\sqrt{12300}=\sqrt{100*123}=\sqrt{100}*\sqrt{123}=10\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{123}}{2*15}=\frac{0-10\sqrt{123}}{30}
=-\frac{10\sqrt{123}}{30}
=-\frac{\sqrt{123}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{123}}{2*15}=\frac{0+10\sqrt{123}}{30}
=\frac{10\sqrt{123}}{30}
=\frac{\sqrt{123}}{3}
$