(21/2)x=17/4

Solution for (21/2)x=17/4 equation:

(21/2)x=17/4

We move all terms to the left:

(21/2)x-(17/4)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+21/2)x-(+17/4)=0

We multiply parentheses

21x^2-(+17/4)=0

We get rid of parentheses

21x^2-17/4=0

We multiply all the terms by the denominator


21x^2*4-17=0

Wy multiply elements

84x^2-17=0

a = 84; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·84·(-17)
Δ = 5712
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:

$\sqrt{\Delta}=\sqrt{5712}=\sqrt{16*357}=\sqrt{16}*\sqrt{357}=4\sqrt{357}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{357}}{2*84}=\frac{0-4\sqrt{357}}{168}
=-\frac{4\sqrt{357}}{168}
=-\frac{\sqrt{357}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{357}}{2*84}=\frac{0+4\sqrt{357}}{168}
=\frac{4\sqrt{357}}{168}
=\frac{\sqrt{357}}{42}
$