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x^2+90x-27000=0
a = 1; b = 90; c = -27000;
Δ = b2-4ac
Δ = 902-4·1·(-27000)
Δ = 116100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116100}=\sqrt{900*129}=\sqrt{900}*\sqrt{129}=30\sqrt{129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-30\sqrt{129}}{2*1}=\frac{-90-30\sqrt{129}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+30\sqrt{129}}{2*1}=\frac{-90+30\sqrt{129}}{2} $
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