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x+(x+7)3x=97
We move all terms to the left:
x+(x+7)3x-(97)=0
We multiply parentheses
3x^2+x+21x-97=0
We add all the numbers together, and all the variables
3x^2+22x-97=0
a = 3; b = 22; c = -97;
Δ = b2-4ac
Δ = 222-4·3·(-97)
Δ = 1648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{103}}{2*3}=\frac{-22-4\sqrt{103}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{103}}{2*3}=\frac{-22+4\sqrt{103}}{6} $
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