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5(29.6-x)x=20
We move all terms to the left:
5(29.6-x)x-(20)=0
We add all the numbers together, and all the variables
5(-1x+29.6)x-20=0
We multiply parentheses
-5x^2+148x-20=0
a = -5; b = 148; c = -20;
Δ = b2-4ac
Δ = 1482-4·(-5)·(-20)
Δ = 21504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21504}=\sqrt{1024*21}=\sqrt{1024}*\sqrt{21}=32\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-32\sqrt{21}}{2*-5}=\frac{-148-32\sqrt{21}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+32\sqrt{21}}{2*-5}=\frac{-148+32\sqrt{21}}{-10} $
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