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13x^2+53.67x=2415.08
We move all terms to the left:
13x^2+53.67x-(2415.08)=0
We add all the numbers together, and all the variables
13x^2+53.67x-2415.08=0
a = 13; b = 53.67; c = -2415.08;
Δ = b2-4ac
Δ = 53.672-4·13·(-2415.08)
Δ = 128464.6289
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{-(53.67)-\sqrt{128464.6289}}{2*13}=\frac{-53.67-\sqrt{128464.6289}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53.67)+\sqrt{128464.6289}}{2*13}=\frac{-53.67+\sqrt{128464.6289}}{26} $
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