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-.02x^2+1500x-37500=0
We add all the numbers together, and all the variables
-0.02x^2+1500x-37500=0
a = -0.02; b = 1500; c = -37500;
Δ = b2-4ac
Δ = 15002-4·(-0.02)·(-37500)
Δ = 2247000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2247000}=\sqrt{100*22470}=\sqrt{100}*\sqrt{22470}=10\sqrt{22470}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-10\sqrt{22470}}{2*-0.02}=\frac{-1500-10\sqrt{22470}}{-0.04} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+10\sqrt{22470}}{2*-0.02}=\frac{-1500+10\sqrt{22470}}{-0.04} $
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