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240000=-2100x+6.5x^2
We move all terms to the left:
240000-(-2100x+6.5x^2)=0
We get rid of parentheses
-6.5x^2+2100x+240000=0
a = -6.5; b = 2100; c = +240000;
Δ = b2-4ac
Δ = 21002-4·(-6.5)·240000
Δ = 10650000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10650000}=\sqrt{10000*1065}=\sqrt{10000}*\sqrt{1065}=100\sqrt{1065}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2100)-100\sqrt{1065}}{2*-6.5}=\frac{-2100-100\sqrt{1065}}{-13} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2100)+100\sqrt{1065}}{2*-6.5}=\frac{-2100+100\sqrt{1065}}{-13} $
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