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180=0.05x^2+1.1x
We move all terms to the left:
180-(0.05x^2+1.1x)=0
We get rid of parentheses
-0.05x^2-1.1x+180=0
a = -0.05; b = -1.1; c = +180;
Δ = b2-4ac
Δ = -1.12-4·(-0.05)·180
Δ = 37.21
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{-(-1.1)-\sqrt{37.21}}{2*-0.05}=\frac{1.1-\sqrt{37.21}}{-0.1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.1)+\sqrt{37.21}}{2*-0.05}=\frac{1.1+\sqrt{37.21}}{-0.1} $
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