((x^2)/40)-(0.1x)-0.9=0

Solution for ((x^2)/40)-(0.1x)-0.9=0 equation:

((x^2)/40)-(0.1x)-0.9=0

We add all the numbers together, and all the variables

(x^2/40)-(+0.1x)-0.9=0

We get rid of parentheses

x^2/40-0.1x-0.9=0

We multiply all the terms by the denominator


x^2-(0.1x)*40-(0.9)*40=0

We add all the numbers together, and all the variables

x^2-(+0.1x)*40-(0.9)*40=0

We add all the numbers together, and all the variables

x^2-(+0.1x)*40-36=0

We multiply parentheses

x^2-0x-36=0

We add all the numbers together, and all the variables

x^2-1x-36=0

a = 1; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·1·(-36)
Δ = 145
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{-(-1)-\sqrt{145}}{2*1}=\frac{1-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*1}=\frac{1+\sqrt{145}}{2}
$