3^x=21/4x-1

Solution for 3^x=21/4x-1 equation:

3^x=21/4x-1

We move all terms to the left:

3^x-(21/4x-1)=0


Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

3^x-21/4x+1=0

We multiply all the terms by the denominator


3^x*4x+1*4x-21=0

Wy multiply elements

12x^2+4x-21=0

a = 12; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·12·(-21)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-32}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+32}{2*12}=\frac{28}{24}
=1+1/6
$