5x(x+6)=-2x(x+6)+28

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Solution for 5x(x+6)=-2x(x+6)+28 equation:



5x(x+6)=-2x(x+6)+28
We move all terms to the left:
5x(x+6)-(-2x(x+6)+28)=0
We multiply parentheses
5x^2+30x-(-2x(x+6)+28)=0
We calculate terms in parentheses: -(-2x(x+6)+28), so:
-2x(x+6)+28
We multiply parentheses
-2x^2-12x+28
Back to the equation:
-(-2x^2-12x+28)
We get rid of parentheses
5x^2+2x^2+12x+30x-28=0
We add all the numbers together, and all the variables
7x^2+42x-28=0
a = 7; b = 42; c = -28;
Δ = b2-4ac
Δ = 422-4·7·(-28)
Δ = 2548
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{2548}=\sqrt{196*13}=\sqrt{196}*\sqrt{13}=14\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14\sqrt{13}}{2*7}=\frac{-42-14\sqrt{13}}{14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14\sqrt{13}}{2*7}=\frac{-42+14\sqrt{13}}{14} $

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