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X^2+12X=6000
We move all terms to the left:
X^2+12X-(6000)=0
a = 1; b = 12; c = -6000;
Δ = b2-4ac
Δ = 122-4·1·(-6000)
Δ = 24144
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24144}=\sqrt{16*1509}=\sqrt{16}*\sqrt{1509}=4\sqrt{1509}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{1509}}{2*1}=\frac{-12-4\sqrt{1509}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{1509}}{2*1}=\frac{-12+4\sqrt{1509}}{2} $
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