x^2+2.75x+1.891=1.4179

Solution for x^2+2.75x+1.891=1.4179 equation:

x^2+2.75x+1.891=1.4179

We move all terms to the left:

x^2+2.75x+1.891-(1.4179)=0

We add all the numbers together, and all the variables

x^2+2.75x+0.4731=0

a = 1; b = 2.75; c = +0.4731;
Δ = b2-4ac
Δ = 2.752-4·1·0.4731
Δ = 5.6701
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{-(2.75)-\sqrt{5.6701}}{2*1}=\frac{-2.75-\sqrt{5.6701}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.75)+\sqrt{5.6701}}{2*1}=\frac{-2.75+\sqrt{5.6701}}{2}
$