5x(.988^x)=2.5

Solution for 5x(.988^x)=2.5 equation:

5x(.988^x)=2.5

We move all terms to the left:

5x(.988^x)-(2.5)=0

We add all the numbers together, and all the variables

5x(.988^x)-2.5=0

We multiply parentheses

5x^2-2.5=0

a = 5; b = 0; c = -2.5;
Δ = b2-4ac
Δ = 02-4·5·(-2.5)
Δ = 50
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:

$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{2}}{2*5}=\frac{0-5\sqrt{2}}{10}
=-\frac{5\sqrt{2}}{10}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{2}}{2*5}=\frac{0+5\sqrt{2}}{10}
=\frac{5\sqrt{2}}{10}
=\frac{\sqrt{2}}{2}
$