195=(2x+13)(2x+21)

Solution for 195=(2x+13)(2x+21) equation:

195=(2x+13)(2x+21)

We move all terms to the left:

195-((2x+13)(2x+21))=0

We multiply parentheses ..

-((+4x^2+42x+26x+273))+195=0


We calculate terms in parentheses: -((+4x^2+42x+26x+273)), so:

(+4x^2+42x+26x+273)

We get rid of parentheses

4x^2+42x+26x+273

We add all the numbers together, and all the variables

4x^2+68x+273

Back to the equation:

-(4x^2+68x+273)


We get rid of parentheses

-4x^2-68x-273+195=0

We add all the numbers together, and all the variables

-4x^2-68x-78=0

a = -4; b = -68; c = -78;
Δ = b2-4ac
Δ = -682-4·(-4)·(-78)
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{211}}{2*-4}=\frac{68-4\sqrt{211}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{211}}{2*-4}=\frac{68+4\sqrt{211}}{-8}
$