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

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

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

We move all terms to the left:

(x+3)(2x-6)-(2600)=0

We multiply parentheses ..

(+2x^2-6x+6x-18)-2600=0

We get rid of parentheses

2x^2-6x+6x-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}
=-\sqrt{1309}
$
$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}
=\sqrt{1309}
$