-1.4x+0.1=4.9x^2

Solution for -1.4x+0.1=4.9x^2 equation:

-1.4x+0.1=4.9x^2

We move all terms to the left:

-1.4x+0.1-(4.9x^2)=0

We get rid of parentheses

-4.9x^2-1.4x+0.1=0

a = -4.9; b = -1.4; c = +0.1;
Δ = b2-4ac
Δ = -1.42-4·(-4.9)·0.1
Δ = 3.92
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{-(-1.4)-\sqrt{3.92}}{2*-4.9}=\frac{1.4-\sqrt{3.92}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.4)+\sqrt{3.92}}{2*-4.9}=\frac{1.4+\sqrt{3.92}}{-9.8}
$