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7a(3a-5)=13
We move all terms to the left:
7a(3a-5)-(13)=0
We multiply parentheses
21a^2-35a-13=0
a = 21; b = -35; c = -13;
Δ = b2-4ac
Δ = -352-4·21·(-13)
Δ = 2317
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{-(-35)-\sqrt{2317}}{2*21}=\frac{35-\sqrt{2317}}{42} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2317}}{2*21}=\frac{35+\sqrt{2317}}{42} $
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