0.51x^2-9.8x=48.02

Solution for 0.51x^2-9.8x=48.02 equation:

0.51x^2-9.8x=48.02

We move all terms to the left:

0.51x^2-9.8x-(48.02)=0

We add all the numbers together, and all the variables

0.51x^2-9.8x-48.02=0

a = 0.51; b = -9.8; c = -48.02;
Δ = b2-4ac
Δ = -9.82-4·0.51·(-48.02)
Δ = 194.0008
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{-(-9.8)-\sqrt{194.0008}}{2*0.51}=\frac{9.8-\sqrt{194.0008}}{1.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.8)+\sqrt{194.0008}}{2*0.51}=\frac{9.8+\sqrt{194.0008}}{1.02}
$