20x(1,05)x=50

Solution for 20x(1,05)x=50 equation:

20x(1.05)x=50

We move all terms to the left:

20x(1.05)x-(50)=0

We multiply parentheses

21x^2-50=0

a = 21; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·21·(-50)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*21}=\frac{0-10\sqrt{42}}{42}
=-\frac{10\sqrt{42}}{42}
=-\frac{5\sqrt{42}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*21}=\frac{0+10\sqrt{42}}{42}
=\frac{10\sqrt{42}}{42}
=\frac{5\sqrt{42}}{21}
$