31x-1.91x2=16x+6

Solution for 31x-1.91x2=16x+6 equation:

31x-1.91x^2=16x+6

We move all terms to the left:

31x-1.91x^2-(16x+6)=0

We get rid of parentheses

-1.91x^2+31x-16x-6=0

We add all the numbers together, and all the variables

-1.91x^2+15x-6=0

a = -1.91; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-1.91)·(-6)
Δ = 179.16
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{-(15)-\sqrt{179.16}}{2*-1.91}=\frac{-15-\sqrt{179.16}}{-3.82}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{179.16}}{2*-1.91}=\frac{-15+\sqrt{179.16}}{-3.82}
$