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x^2+.5x=288
We move all terms to the left:
x^2+.5x-(288)=0
a = 1; b = .5; c = -288;
Δ = b2-4ac
Δ = .52-4·1·(-288)
Δ = 1152.25
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{1152.25}}{2*1}=\frac{-0.5-\sqrt{1152.25}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.5)+\sqrt{1152.25}}{2*1}=\frac{-0.5+\sqrt{1152.25}}{2} $
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