3*2.718^(3x)=15x^2

Solution for 3*2.718^(3x)=15x^2 equation:

3*2.718^(3x)=15x^2

We move all terms to the left:

3*2.718^(3x)-(15x^2)=0

determiningTheFunctionDomain
-15x^2+3*2.718^3x=0

Wy multiply elements

-15x^2+6x=0

a = -15; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-15)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-15}=\frac{-12}{-30}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-15}=\frac{0}{-30}
=0
$