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4.15x+8x^2=-0.05
We move all terms to the left:
4.15x+8x^2-(-0.05)=0
We add all the numbers together, and all the variables
8x^2+4.15x+0.05=0
a = 8; b = 4.15; c = +0.05;
Δ = b2-4ac
Δ = 4.152-4·8·0.05
Δ = 15.6225
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{-(4.15)-\sqrt{15.6225}}{2*8}=\frac{-4.15-\sqrt{15.6225}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.15)+\sqrt{15.6225}}{2*8}=\frac{-4.15+\sqrt{15.6225}}{16} $
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