5x^2+9.8x=10x^2+4.9x

Solution for 5x^2+9.8x=10x^2+4.9x equation:

5x^2+9.8x=10x^2+4.9x

We move all terms to the left:

5x^2+9.8x-(10x^2+4.9x)=0

We get rid of parentheses

5x^2-10x^2+9.8x-4.9x=0

We add all the numbers together, and all the variables

-5x^2+4.9x=0

a = -5; b = 4.9; c = 0;
Δ = b2-4ac
Δ = 4.92-4·(-5)·0
Δ = 24.01
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{24.01}}{2*-5}=\frac{-4.9-\sqrt{24.01}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.9)+\sqrt{24.01}}{2*-5}=\frac{-4.9+\sqrt{24.01}}{-10}
$