3x-18/3^x=7

Solution for 3x-18/3^x=7 equation:

3x-18/3^x=7

We move all terms to the left:

3x-18/3^x-(7)=0


Domain of the equation: 3^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


3x*3^x-7*3^x-18=0

Wy multiply elements

9x^2-21x-18=0

a = 9; b = -21; c = -18;
Δ = b2-4ac
Δ = -212-4·9·(-18)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-33}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+33}{2*9}=\frac{54}{18}
=3
$