x*0.975^x=0.5x

Solution for x*0.975^x=0.5x equation:

x*0.975^x=0.5x

We move all terms to the left:

x*0.975^x-(0.5x)=0

We add all the numbers together, and all the variables

x*0.975^x-(+0.5x)=0

Wy multiply elements

0x^2-(+0.5x)=0

We get rid of parentheses

0x^2-0.5x=0

We add all the numbers together, and all the variables

x^2-0.5x=0

a = 1; b = -0.5; c = 0;
Δ = b2-4ac
Δ = -0.52-4·1·0
Δ = 0.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.5)-\sqrt{0.25}}{2*1}=\frac{0.5-\sqrt{0.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.25}}{2*1}=\frac{0.5+\sqrt{0.25}}{2}
$