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x^2+45x+281.25=0
a = 1; b = 45; c = +281.25;
Δ = b2-4ac
Δ = 452-4·1·281.25
Δ = 900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-30}{2*1}=\frac{-75}{2} =-37+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+30}{2*1}=\frac{-15}{2} =-7+1/2 $
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