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(x+75)(40+x)=9000
We move all terms to the left:
(x+75)(40+x)-(9000)=0
We add all the numbers together, and all the variables
(x+75)(x+40)-9000=0
We multiply parentheses ..
(+x^2+40x+75x+3000)-9000=0
We get rid of parentheses
x^2+40x+75x+3000-9000=0
We add all the numbers together, and all the variables
x^2+115x-6000=0
a = 1; b = 115; c = -6000;
Δ = b2-4ac
Δ = 1152-4·1·(-6000)
Δ = 37225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{37225}=\sqrt{25*1489}=\sqrt{25}*\sqrt{1489}=5\sqrt{1489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-5\sqrt{1489}}{2*1}=\frac{-115-5\sqrt{1489}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+5\sqrt{1489}}{2*1}=\frac{-115+5\sqrt{1489}}{2} $
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