76.6x+x^2=0.5/0.114

Solution for 76.6x+x^2=0.5/0.114 equation:

76.6x+x^2=0.5/0.114

We move all terms to the left:

76.6x+x^2-(0.5/0.114)=0

We add all the numbers together, and all the variables

x^2+76.6x-(+0.5/0.114)=0

We get rid of parentheses

x^2+76.6x-0.5/0.114=0

We multiply all the terms by the denominator


x^2*0.114+(76.6x)*0.114-0.5=0

We add all the numbers together, and all the variables

x^2*0.114+(+76.6x)*0.114-0.5=0

We multiply parentheses

x^2*0.114+8.664x-0.5=0

Wy multiply elements

0.114x^2+8.664x-0.5=0

a = 0.114; b = 8.664; c = -0.5;
Δ = b2-4ac
Δ = 8.6642-4·0.114·(-0.5)
Δ = 75.292896
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{-(8.664)-\sqrt{75.292896}}{2*0.114}=\frac{-8.664-\sqrt{75.292896}}{0.228}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.664)+\sqrt{75.292896}}{2*0.114}=\frac{-8.664+\sqrt{75.292896}}{0.228}
$