10x^2-x-0.9=0

Solution for 10x^2-x-0.9=0 equation:

10x^2-x-0.9=0

We add all the numbers together, and all the variables

10x^2-1x-0.9=0

a = 10; b = -1; c = -0.9;
Δ = b2-4ac
Δ = -12-4·10·(-0.9)
Δ = 37
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{37}}{2*10}=\frac{1-\sqrt{37}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*10}=\frac{1+\sqrt{37}}{20}
$