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55x+60x(7-x)=405
We move all terms to the left:
55x+60x(7-x)-(405)=0
We add all the numbers together, and all the variables
55x+60x(-1x+7)-405=0
We multiply parentheses
-60x^2+55x+420x-405=0
We add all the numbers together, and all the variables
-60x^2+475x-405=0
a = -60; b = 475; c = -405;
Δ = b2-4ac
Δ = 4752-4·(-60)·(-405)
Δ = 128425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{128425}=\sqrt{25*5137}=\sqrt{25}*\sqrt{5137}=5\sqrt{5137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(475)-5\sqrt{5137}}{2*-60}=\frac{-475-5\sqrt{5137}}{-120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(475)+5\sqrt{5137}}{2*-60}=\frac{-475+5\sqrt{5137}}{-120} $
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