1.67x^2+x=1.9

Solution for 1.67x^2+x=1.9 equation:

1.67x^2+x=1.9

We move all terms to the left:

1.67x^2+x-(1.9)=0

We add all the numbers together, and all the variables

1.67x^2+x-1.9=0

a = 1.67; b = 1; c = -1.9;
Δ = b2-4ac
Δ = 12-4·1.67·(-1.9)
Δ = 13.692
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{13.692}}{2*1.67}=\frac{-1-\sqrt{13.692}}{3.34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13.692}}{2*1.67}=\frac{-1+\sqrt{13.692}}{3.34}
$