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564-7.48x+0.029x^2=115
We move all terms to the left:
564-7.48x+0.029x^2-(115)=0
We add all the numbers together, and all the variables
0.029x^2-7.48x+449=0
a = 0.029; b = -7.48; c = +449;
Δ = b2-4ac
Δ = -7.482-4·0.029·449
Δ = 3.8664
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{-(-7.48)-\sqrt{3.8664}}{2*0.029}=\frac{7.48-\sqrt{3.8664}}{0.058} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.48)+\sqrt{3.8664}}{2*0.029}=\frac{7.48+\sqrt{3.8664}}{0.058} $
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