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11=5x+4.095x^2
We move all terms to the left:
11-(5x+4.095x^2)=0
We get rid of parentheses
-4.095x^2-5x+11=0
a = -4.095; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-4.095)·11
Δ = 205.18
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)-\sqrt{205.18}}{2*-4.095}=\frac{5-\sqrt{205.18}}{-8.19} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{205.18}}{2*-4.095}=\frac{5+\sqrt{205.18}}{-8.19} $
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