(3/10)x=101/2

Solution for (3/10)x=101/2 equation:

(3/10)x=101/2

We move all terms to the left:

(3/10)x-(101/2)=0


Domain of the equation: 10)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/10)x-(+101/2)=0

We multiply parentheses

3x^2-(+101/2)=0

We get rid of parentheses

3x^2-101/2=0

We multiply all the terms by the denominator


3x^2*2-101=0

Wy multiply elements

6x^2-101=0

a = 6; b = 0; c = -101;
Δ = b2-4ac
Δ = 02-4·6·(-101)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{606}}{2*6}=\frac{0-2\sqrt{606}}{12}
=-\frac{2\sqrt{606}}{12}
=-\frac{\sqrt{606}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{606}}{2*6}=\frac{0+2\sqrt{606}}{12}
=\frac{2\sqrt{606}}{12}
=\frac{\sqrt{606}}{6}
$