(a+6)(2a-1)=2a+11a

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Solution for (a+6)(2a-1)=2a+11a equation:



(a+6)(2a-1)=2a+11a
We move all terms to the left:
(a+6)(2a-1)-(2a+11a)=0
We add all the numbers together, and all the variables
(a+6)(2a-1)-(+13a)=0
We get rid of parentheses
(a+6)(2a-1)-13a=0
We multiply parentheses ..
(+2a^2-1a+12a-6)-13a=0
We get rid of parentheses
2a^2-1a+12a-13a-6=0
We add all the numbers together, and all the variables
2a^2-2a-6=0
a = 2; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·2·(-6)
Δ = 52
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:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*2}=\frac{2-2\sqrt{13}}{4} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*2}=\frac{2+2\sqrt{13}}{4} $

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