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1.5=-4.9x^2+19.6x+58.8
We move all terms to the left:
1.5-(-4.9x^2+19.6x+58.8)=0
We get rid of parentheses
4.9x^2-19.6x-58.8+1.5=0
We add all the numbers together, and all the variables
4.9x^2-19.6x-57.3=0
a = 4.9; b = -19.6; c = -57.3;
Δ = b2-4ac
Δ = -19.62-4·4.9·(-57.3)
Δ = 1507.24
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{-(-19.6)-\sqrt{1507.24}}{2*4.9}=\frac{19.6-\sqrt{1507.24}}{9.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.6)+\sqrt{1507.24}}{2*4.9}=\frac{19.6+\sqrt{1507.24}}{9.8} $
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