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3=-16x^2+30.4x+5
We move all terms to the left:
3-(-16x^2+30.4x+5)=0
We get rid of parentheses
16x^2-30.4x-5+3=0
We add all the numbers together, and all the variables
16x^2-30.4x-2=0
a = 16; b = -30.4; c = -2;
Δ = b2-4ac
Δ = -30.42-4·16·(-2)
Δ = 1052.16
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{-(-30.4)-\sqrt{1052.16}}{2*16}=\frac{30.4-\sqrt{1052.16}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30.4)+\sqrt{1052.16}}{2*16}=\frac{30.4+\sqrt{1052.16}}{32} $
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