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a(a+64)=180
We move all terms to the left:
a(a+64)-(180)=0
We multiply parentheses
a^2+64a-180=0
a = 1; b = 64; c = -180;
Δ = b2-4ac
Δ = 642-4·1·(-180)
Δ = 4816
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4816}=\sqrt{16*301}=\sqrt{16}*\sqrt{301}=4\sqrt{301}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{301}}{2*1}=\frac{-64-4\sqrt{301}}{2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{301}}{2*1}=\frac{-64+4\sqrt{301}}{2} $
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