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275x-x2-2000=3750
We move all terms to the left:
275x-x2-2000-(3750)=0
We add all the numbers together, and all the variables
-1x^2+275x-5750=0
a = -1; b = 275; c = -5750;
Δ = b2-4ac
Δ = 2752-4·(-1)·(-5750)
Δ = 52625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52625}=\sqrt{25*2105}=\sqrt{25}*\sqrt{2105}=5\sqrt{2105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(275)-5\sqrt{2105}}{2*-1}=\frac{-275-5\sqrt{2105}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(275)+5\sqrt{2105}}{2*-1}=\frac{-275+5\sqrt{2105}}{-2} $
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