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(70+4x)(50-x)=2000
We move all terms to the left:
(70+4x)(50-x)-(2000)=0
We add all the numbers together, and all the variables
(4x+70)(-1x+50)-2000=0
We multiply parentheses ..
(-4x^2+200x-70x+3500)-2000=0
We get rid of parentheses
-4x^2+200x-70x+3500-2000=0
We add all the numbers together, and all the variables
-4x^2+130x+1500=0
a = -4; b = 130; c = +1500;
Δ = b2-4ac
Δ = 1302-4·(-4)·1500
Δ = 40900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40900}=\sqrt{100*409}=\sqrt{100}*\sqrt{409}=10\sqrt{409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-10\sqrt{409}}{2*-4}=\frac{-130-10\sqrt{409}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+10\sqrt{409}}{2*-4}=\frac{-130+10\sqrt{409}}{-8} $
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