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198.5=4x+3.14x^2
We move all terms to the left:
198.5-(4x+3.14x^2)=0
We get rid of parentheses
-3.14x^2-4x+198.5=0
a = -3.14; b = -4; c = +198.5;
Δ = b2-4ac
Δ = -42-4·(-3.14)·198.5
Δ = 2509.16
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)-\sqrt{2509.16}}{2*-3.14}=\frac{4-\sqrt{2509.16}}{-6.28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{2509.16}}{2*-3.14}=\frac{4+\sqrt{2509.16}}{-6.28} $
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