5*3^2x=10*2^x

Solution for 5*3^2x=10*2^x equation:

5*3^2x=10*2^x

We move all terms to the left:

5*3^2x-(10*2^x)=0

Wy multiply elements

15x^2-(10*2^x)=0

We get rid of parentheses

15x^2-10*2^x=0

Wy multiply elements

15x^2-20x=0

a = 15; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·15·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*15}=\frac{40}{30}
=1+1/3
$