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8x+4.19x^2=12
We move all terms to the left:
8x+4.19x^2-(12)=0
a = 4.19; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·4.19·(-12)
Δ = 265.12
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{-(8)-\sqrt{265.12}}{2*4.19}=\frac{-8-\sqrt{265.12}}{8.38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+\sqrt{265.12}}{2*4.19}=\frac{-8+\sqrt{265.12}}{8.38} $
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