2600=(2x-6)(x+3)

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Solution for 2600=(2x-6)(x+3) equation:



2600=(2x-6)(x+3)
We move all terms to the left:
2600-((2x-6)(x+3))=0
We multiply parentheses ..
-((+2x^2+6x-6x-18))+2600=0
We calculate terms in parentheses: -((+2x^2+6x-6x-18)), so:
(+2x^2+6x-6x-18)
We get rid of parentheses
2x^2+6x-6x-18
We add all the numbers together, and all the variables
2x^2-18
Back to the equation:
-(2x^2-18)
We get rid of parentheses
-2x^2+18+2600=0
We add all the numbers together, and all the variables
-2x^2+2618=0
a = -2; b = 0; c = +2618;
Δ = b2-4ac
Δ = 02-4·(-2)·2618
Δ = 20944
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:
$\sqrt{\Delta}=\sqrt{20944}=\sqrt{16*1309}=\sqrt{16}*\sqrt{1309}=4\sqrt{1309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1309}}{2*-2}=\frac{0-4\sqrt{1309}}{-4} =-\frac{4\sqrt{1309}}{-4} =-\frac{\sqrt{1309}}{-1} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1309}}{2*-2}=\frac{0+4\sqrt{1309}}{-4} =\frac{4\sqrt{1309}}{-4} =\frac{\sqrt{1309}}{-1} $

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