(2x+13)(2x+21)=78

Solution for (2x+13)(2x+21)=78 equation:

(2x+13)(2x+21)=78

We move all terms to the left:

(2x+13)(2x+21)-(78)=0

We multiply parentheses ..

(+4x^2+42x+26x+273)-78=0

We get rid of parentheses

4x^2+42x+26x+273-78=0

We add all the numbers together, and all the variables

4x^2+68x+195=0

a = 4; b = 68; c = +195;
Δ = b2-4ac
Δ = 682-4·4·195
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{94}}{2*4}=\frac{-68-4\sqrt{94}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{94}}{2*4}=\frac{-68+4\sqrt{94}}{8}
$