x=21/4,x=-11/4

Solution for x=21/4,x=-11/4 equation:

x=21/4.x=-11/4

We move all terms to the left:

x-(21/4.x)=0


Domain of the equation: 4.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+21/4.x)=0

We get rid of parentheses

x-21/4.x=0

We multiply all the terms by the denominator


x*4.x-21=0

Wy multiply elements

4x^2-21=0

a = 4; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·4·(-21)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*4}=\frac{0-4\sqrt{21}}{8}
=-\frac{4\sqrt{21}}{8}
=-\frac{\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*4}=\frac{0+4\sqrt{21}}{8}
=\frac{4\sqrt{21}}{8}
=\frac{\sqrt{21}}{2}
$