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2a(5a-4)=4
We move all terms to the left:
2a(5a-4)-(4)=0
We multiply parentheses
10a^2-8a-4=0
a = 10; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·10·(-4)
Δ = 224
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{14}}{2*10}=\frac{8-4\sqrt{14}}{20} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{14}}{2*10}=\frac{8+4\sqrt{14}}{20} $
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