0.17x^2=2x+1

Solution for 0.17x^2=2x+1 equation:

0.17x^2=2x+1

We move all terms to the left:

0.17x^2-(2x+1)=0

We get rid of parentheses

0.17x^2-2x-1=0

a = 0.17; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·0.17·(-1)
Δ = 4.68
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{-(-2)-\sqrt{4.68}}{2*0.17}=\frac{2-\sqrt{4.68}}{0.34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{4.68}}{2*0.17}=\frac{2+\sqrt{4.68}}{0.34}
$