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6x^2+5000x=45677
We move all terms to the left:
6x^2+5000x-(45677)=0
a = 6; b = 5000; c = -45677;
Δ = b2-4ac
Δ = 50002-4·6·(-45677)
Δ = 26096248
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26096248}=\sqrt{4*6524062}=\sqrt{4}*\sqrt{6524062}=2\sqrt{6524062}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-2\sqrt{6524062}}{2*6}=\frac{-5000-2\sqrt{6524062}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+2\sqrt{6524062}}{2*6}=\frac{-5000+2\sqrt{6524062}}{12} $
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