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10=5.7x-4.7x^2+8.7
We move all terms to the left:
10-(5.7x-4.7x^2+8.7)=0
We get rid of parentheses
4.7x^2-5.7x-8.7+10=0
We add all the numbers together, and all the variables
4.7x^2-5.7x+1.3=0
a = 4.7; b = -5.7; c = +1.3;
Δ = b2-4ac
Δ = -5.72-4·4.7·1.3
Δ = 8.05
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{-(-5.7)-\sqrt{8.05}}{2*4.7}=\frac{5.7-\sqrt{8.05}}{9.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.7)+\sqrt{8.05}}{2*4.7}=\frac{5.7+\sqrt{8.05}}{9.4} $
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