34=(2x+10)(x+2)

Solution for 34=(2x+10)(x+2) equation:

34=(2x+10)(x+2)

We move all terms to the left:

34-((2x+10)(x+2))=0

We multiply parentheses ..

-((+2x^2+4x+10x+20))+34=0


We calculate terms in parentheses: -((+2x^2+4x+10x+20)), so:

(+2x^2+4x+10x+20)

We get rid of parentheses

2x^2+4x+10x+20

We add all the numbers together, and all the variables

2x^2+14x+20

Back to the equation:

-(2x^2+14x+20)


We get rid of parentheses

-2x^2-14x-20+34=0

We add all the numbers together, and all the variables

-2x^2-14x+14=0

a = -2; b = -14; c = +14;
Δ = b2-4ac
Δ = -142-4·(-2)·14
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{77}}{2*-2}=\frac{14-2\sqrt{77}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{77}}{2*-2}=\frac{14+2\sqrt{77}}{-4}
$