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(30+4x)(50-x)=2000
We move all terms to the left:
(30+4x)(50-x)-(2000)=0
We add all the numbers together, and all the variables
(4x+30)(-1x+50)-2000=0
We multiply parentheses ..
(-4x^2+200x-30x+1500)-2000=0
We get rid of parentheses
-4x^2+200x-30x+1500-2000=0
We add all the numbers together, and all the variables
-4x^2+170x-500=0
a = -4; b = 170; c = -500;
Δ = b2-4ac
Δ = 1702-4·(-4)·(-500)
Δ = 20900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20900}=\sqrt{100*209}=\sqrt{100}*\sqrt{209}=10\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-10\sqrt{209}}{2*-4}=\frac{-170-10\sqrt{209}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+10\sqrt{209}}{2*-4}=\frac{-170+10\sqrt{209}}{-8} $
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