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(60-2x)(40-2x)=176000
We move all terms to the left:
(60-2x)(40-2x)-(176000)=0
We add all the numbers together, and all the variables
(-2x+60)(-2x+40)-176000=0
We multiply parentheses ..
(+4x^2-80x-120x+2400)-176000=0
We get rid of parentheses
4x^2-80x-120x+2400-176000=0
We add all the numbers together, and all the variables
4x^2-200x-173600=0
a = 4; b = -200; c = -173600;
Δ = b2-4ac
Δ = -2002-4·4·(-173600)
Δ = 2817600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2817600}=\sqrt{1600*1761}=\sqrt{1600}*\sqrt{1761}=40\sqrt{1761}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{1761}}{2*4}=\frac{200-40\sqrt{1761}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{1761}}{2*4}=\frac{200+40\sqrt{1761}}{8} $
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