x^2+x=1/4.9

Solution for x^2+x=1/4.9 equation:

x^2+x=1/4.9

We move all terms to the left:

x^2+x-(1/4.9)=0

We add all the numbers together, and all the variables

x^2+x-(+1/4.9)=0

We get rid of parentheses

x^2+x-1/4.9=0

We multiply all the terms by the denominator


x^2*4.9+x*4.9-1=0

Wy multiply elements

4.9x^2+4.9x-1=0

a = 4.9; b = 4.9; c = -1;
Δ = b2-4ac
Δ = 4.92-4·4.9·(-1)
Δ = 43.61
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{-(4.9)-\sqrt{43.61}}{2*4.9}=\frac{-4.9-\sqrt{43.61}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.9)+\sqrt{43.61}}{2*4.9}=\frac{-4.9+\sqrt{43.61}}{9.8}
$