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0=20+50x-4.9x^2
We move all terms to the left:
0-(20+50x-4.9x^2)=0
We add all the numbers together, and all the variables
-(20+50x-4.9x^2)=0
We get rid of parentheses
4.9x^2-50x-20=0
a = 4.9; b = -50; c = -20;
Δ = b2-4ac
Δ = -502-4·4.9·(-20)
Δ = 2892
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{723}}{2*4.9}=\frac{50-2\sqrt{723}}{9.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{723}}{2*4.9}=\frac{50+2\sqrt{723}}{9.8} $
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