1.4x^2-3.1x=1

Solution for 1.4x^2-3.1x=1 equation:

1.4x^2-3.1x=1

We move all terms to the left:

1.4x^2-3.1x-(1)=0

a = 1.4; b = -3.1; c = -1;
Δ = b2-4ac
Δ = -3.12-4·1.4·(-1)
Δ = 15.21
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{-(-3.1)-\sqrt{15.21}}{2*1.4}=\frac{3.1-\sqrt{15.21}}{2.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.1)+\sqrt{15.21}}{2*1.4}=\frac{3.1+\sqrt{15.21}}{2.8}
$