10^x*3^x+15=20

Solution for 10^x*3^x+15=20 equation:

10^x*3^x+15=20

We move all terms to the left:

10^x*3^x+15-(20)=0

We add all the numbers together, and all the variables

10^x*3^x-5=0

Wy multiply elements

30x^2-5=0

a = 30; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·30·(-5)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*30}=\frac{0-10\sqrt{6}}{60}
=-\frac{10\sqrt{6}}{60}
=-\frac{\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*30}=\frac{0+10\sqrt{6}}{60}
=\frac{10\sqrt{6}}{60}
=\frac{\sqrt{6}}{6}
$