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2a(5+4a)=20
We move all terms to the left:
2a(5+4a)-(20)=0
We add all the numbers together, and all the variables
2a(4a+5)-20=0
We multiply parentheses
8a^2+10a-20=0
a = 8; b = 10; c = -20;
Δ = b2-4ac
Δ = 102-4·8·(-20)
Δ = 740
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{185}}{2*8}=\frac{-10-2\sqrt{185}}{16} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{185}}{2*8}=\frac{-10+2\sqrt{185}}{16} $
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