(350-10x-200)(20x+150)=25000

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Solution for (350-10x-200)(20x+150)=25000 equation:



(350-10x-200)(20x+150)=25000
We move all terms to the left:
(350-10x-200)(20x+150)-(25000)=0
We add all the numbers together, and all the variables
(-10x+150)(20x+150)-25000=0
We multiply parentheses ..
(-200x^2-1500x+3000x+22500)-25000=0
We get rid of parentheses
-200x^2-1500x+3000x+22500-25000=0
We add all the numbers together, and all the variables
-200x^2+1500x-2500=0
a = -200; b = 1500; c = -2500;
Δ = b2-4ac
Δ = 15002-4·(-200)·(-2500)
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-500}{2*-200}=\frac{-2000}{-400} =+5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+500}{2*-200}=\frac{-1000}{-400} =2+1/2 $

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