4x-21/2x=6

Solution for 4x-21/2x=6 equation:

4x-21/2x=6

We move all terms to the left:

4x-21/2x-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-6*2x-21=0

Wy multiply elements

8x^2-12x-21=0

a = 8; b = -12; c = -21;
Δ = b2-4ac
Δ = -122-4·8·(-21)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{51}}{2*8}=\frac{12-4\sqrt{51}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{51}}{2*8}=\frac{12+4\sqrt{51}}{16}
$