12x+49=21/4x

Solution for 12x+49=21/4x equation:

12x+49=21/4x

We move all terms to the left:

12x+49-(21/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(+21/4x)+49=0

We get rid of parentheses

12x-21/4x+49=0

We multiply all the terms by the denominator


12x*4x+49*4x-21=0

Wy multiply elements

48x^2+196x-21=0

a = 48; b = 196; c = -21;
Δ = b2-4ac
Δ = 1962-4·48·(-21)
Δ = 42448
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:

$\sqrt{\Delta}=\sqrt{42448}=\sqrt{16*2653}=\sqrt{16}*\sqrt{2653}=4\sqrt{2653}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{2653}}{2*48}=\frac{-196-4\sqrt{2653}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{2653}}{2*48}=\frac{-196+4\sqrt{2653}}{96}
$