269=2x^2-3.9x+85

Solution for 269=2x^2-3.9x+85 equation:

269=2x^2-3.9x+85

We move all terms to the left:

269-(2x^2-3.9x+85)=0

We get rid of parentheses

-2x^2+3.9x-85+269=0

We add all the numbers together, and all the variables

-2x^2+3.9x+184=0

a = -2; b = 3.9; c = +184;
Δ = b2-4ac
Δ = 3.92-4·(-2)·184
Δ = 1487.21
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{-(3.9)-\sqrt{1487.21}}{2*-2}=\frac{-3.9-\sqrt{1487.21}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.9)+\sqrt{1487.21}}{2*-2}=\frac{-3.9+\sqrt{1487.21}}{-4}
$