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14=-0.1x^2+30x
We move all terms to the left:
14-(-0.1x^2+30x)=0
We get rid of parentheses
0.1x^2-30x+14=0
a = 0.1; b = -30; c = +14;
Δ = b2-4ac
Δ = -302-4·0.1·14
Δ = 894.4
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{-(-30)-\sqrt{894.4}}{2*0.1}=\frac{30-\sqrt{894.4}}{0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{894.4}}{2*0.1}=\frac{30+\sqrt{894.4}}{0.2} $
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