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7a(3a-3)=19
We move all terms to the left:
7a(3a-3)-(19)=0
We multiply parentheses
21a^2-21a-19=0
a = 21; b = -21; c = -19;
Δ = b2-4ac
Δ = -212-4·21·(-19)
Δ = 2037
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{2037}}{2*21}=\frac{21-\sqrt{2037}}{42} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{2037}}{2*21}=\frac{21+\sqrt{2037}}{42} $
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