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7x(x-3)-7x-21=0
We add all the numbers together, and all the variables
-7x+7x(x-3)-21=0
We multiply parentheses
7x^2-7x-21x-21=0
We add all the numbers together, and all the variables
7x^2-28x-21=0
a = 7; b = -28; c = -21;
Δ = b2-4ac
Δ = -282-4·7·(-21)
Δ = 1372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-14\sqrt{7}}{2*7}=\frac{28-14\sqrt{7}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+14\sqrt{7}}{2*7}=\frac{28+14\sqrt{7}}{14} $
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