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8a(-2a-10)=2a-2
We move all terms to the left:
8a(-2a-10)-(2a-2)=0
We multiply parentheses
-16a^2-80a-(2a-2)=0
We get rid of parentheses
-16a^2-80a-2a+2=0
We add all the numbers together, and all the variables
-16a^2-82a+2=0
a = -16; b = -82; c = +2;
Δ = b2-4ac
Δ = -822-4·(-16)·2
Δ = 6852
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6852}=\sqrt{4*1713}=\sqrt{4}*\sqrt{1713}=2\sqrt{1713}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1713}}{2*-16}=\frac{82-2\sqrt{1713}}{-32} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1713}}{2*-16}=\frac{82+2\sqrt{1713}}{-32} $
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