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(x-6)(250-5x)=6
We move all terms to the left:
(x-6)(250-5x)-(6)=0
We add all the numbers together, and all the variables
(x-6)(-5x+250)-6=0
We multiply parentheses ..
(-5x^2+250x+30x-1500)-6=0
We get rid of parentheses
-5x^2+250x+30x-1500-6=0
We add all the numbers together, and all the variables
-5x^2+280x-1506=0
a = -5; b = 280; c = -1506;
Δ = b2-4ac
Δ = 2802-4·(-5)·(-1506)
Δ = 48280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{48280}=\sqrt{4*12070}=\sqrt{4}*\sqrt{12070}=2\sqrt{12070}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-2\sqrt{12070}}{2*-5}=\frac{-280-2\sqrt{12070}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+2\sqrt{12070}}{2*-5}=\frac{-280+2\sqrt{12070}}{-10} $
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