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x(2)+5(20-x)=49x=17
We move all terms to the left:
x(2)+5(20-x)-(49x)=0
We add all the numbers together, and all the variables
x2+5(-1x+20)-49x=0
We add all the numbers together, and all the variables
x^2-49x+5(-1x+20)=0
We multiply parentheses
x^2-49x-5x+100=0
We add all the numbers together, and all the variables
x^2-54x+100=0
a = 1; b = -54; c = +100;
Δ = b2-4ac
Δ = -542-4·1·100
Δ = 2516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2516}=\sqrt{4*629}=\sqrt{4}*\sqrt{629}=2\sqrt{629}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{629}}{2*1}=\frac{54-2\sqrt{629}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{629}}{2*1}=\frac{54+2\sqrt{629}}{2} $
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