x=4.905x^2+5x-11

Solution for x=4.905x^2+5x-11 equation:

x=4.905x^2+5x-11

We move all terms to the left:

x-(4.905x^2+5x-11)=0

We get rid of parentheses

-4.905x^2+x-5x+11=0

We add all the numbers together, and all the variables

-4.905x^2-4x+11=0

a = -4.905; b = -4; c = +11;
Δ = b2-4ac
Δ = -42-4·(-4.905)·11
Δ = 231.82
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)-\sqrt{231.82}}{2*-4.905}=\frac{4-\sqrt{231.82}}{-9.81}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{231.82}}{2*-4.905}=\frac{4+\sqrt{231.82}}{-9.81}
$