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9x^2+3x-7x-21=0
We add all the numbers together, and all the variables
9x^2-4x-21=0
a = 9; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·9·(-21)
Δ = 772
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{193}}{2*9}=\frac{4-2\sqrt{193}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{193}}{2*9}=\frac{4+2\sqrt{193}}{18} $
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