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0.8x^2+5.2x+1=-4.6
We move all terms to the left:
0.8x^2+5.2x+1-(-4.6)=0
We add all the numbers together, and all the variables
0.8x^2+5.2x+5.6=0
a = 0.8; b = 5.2; c = +5.6;
Δ = b2-4ac
Δ = 5.22-4·0.8·5.6
Δ = 9.12
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{-(5.2)-\sqrt{9.12}}{2*0.8}=\frac{-5.2-\sqrt{9.12}}{1.6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.2)+\sqrt{9.12}}{2*0.8}=\frac{-5.2+\sqrt{9.12}}{1.6} $
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