3^x=15/4^x

Solution for 3^x=15/4^x equation:

3^x=15/4^x

We move all terms to the left:

3^x-(15/4^x)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

3^x-15/4^x=0

We multiply all the terms by the denominator


3^x*4^x-15=0

Wy multiply elements

12x^2-15=0

a = 12; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·12·(-15)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*12}=\frac{0-12\sqrt{5}}{24}
=-\frac{12\sqrt{5}}{24}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*12}=\frac{0+12\sqrt{5}}{24}
=\frac{12\sqrt{5}}{24}
=\frac{\sqrt{5}}{2}
$