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2a(2+a)+44=180
We move all terms to the left:
2a(2+a)+44-(180)=0
We add all the numbers together, and all the variables
2a(a+2)+44-180=0
We add all the numbers together, and all the variables
2a(a+2)-136=0
We multiply parentheses
2a^2+4a-136=0
a = 2; b = 4; c = -136;
Δ = b2-4ac
Δ = 42-4·2·(-136)
Δ = 1104
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{69}}{2*2}=\frac{-4-4\sqrt{69}}{4} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{69}}{2*2}=\frac{-4+4\sqrt{69}}{4} $
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