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2(a-1)5a=7
We move all terms to the left:
2(a-1)5a-(7)=0
We multiply parentheses
10a^2-10a-7=0
a = 10; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·10·(-7)
Δ = 380
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{95}}{2*10}=\frac{10-2\sqrt{95}}{20} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{95}}{2*10}=\frac{10+2\sqrt{95}}{20} $
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