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7x(x+32)=259
We move all terms to the left:
7x(x+32)-(259)=0
We multiply parentheses
7x^2+224x-259=0
a = 7; b = 224; c = -259;
Δ = b2-4ac
Δ = 2242-4·7·(-259)
Δ = 57428
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57428}=\sqrt{196*293}=\sqrt{196}*\sqrt{293}=14\sqrt{293}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-14\sqrt{293}}{2*7}=\frac{-224-14\sqrt{293}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+14\sqrt{293}}{2*7}=\frac{-224+14\sqrt{293}}{14} $
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