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9x^2+3x-7x-21=-9
We move all terms to the left:
9x^2+3x-7x-21-(-9)=0
We add all the numbers together, and all the variables
9x^2-4x-12=0
a = 9; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·9·(-12)
Δ = 448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{7}}{2*9}=\frac{4-8\sqrt{7}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{7}}{2*9}=\frac{4+8\sqrt{7}}{18} $
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