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176=0.05x+x^2
We move all terms to the left:
176-(0.05x+x^2)=0
We get rid of parentheses
-x^2-0.05x+176=0
We add all the numbers together, and all the variables
-1x^2-0.05x+176=0
a = -1; b = -0.05; c = +176;
Δ = b2-4ac
Δ = -0.052-4·(-1)·176
Δ = 704.0025
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{-(-0.05)-\sqrt{704.0025}}{2*-1}=\frac{0.05-\sqrt{704.0025}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{704.0025}}{2*-1}=\frac{0.05+\sqrt{704.0025}}{-2} $
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