x+x^2/8.28=5.75

Solution for x+x^2/8.28=5.75 equation:

x+x^2/8.28=5.75

We move all terms to the left:

x+x^2/8.28-(5.75)=0

We add all the numbers together, and all the variables

x^2/8.28+x-5.75=0

We multiply all the terms by the denominator


x^2+x*8.28-(5.75)*8.28=0

We add all the numbers together, and all the variables

x^2+x*8.28-47.61=0

Wy multiply elements

x^2+8.28x-47.61=0

a = 1; b = 8.28; c = -47.61;
Δ = b2-4ac
Δ = 8.282-4·1·(-47.61)
Δ = 258.9984
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{-(8.28)-\sqrt{258.9984}}{2*1}=\frac{-8.28-\sqrt{258.9984}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.28)+\sqrt{258.9984}}{2*1}=\frac{-8.28+\sqrt{258.9984}}{2}
$