2(x+3)(x+9)=374

Solution for 2(x+3)(x+9)=374 equation:

2(x+3)(x+9)=374

We move all terms to the left:

2(x+3)(x+9)-(374)=0

We multiply parentheses ..

2(+x^2+9x+3x+27)-374=0

We multiply parentheses

2x^2+18x+6x+54-374=0

We add all the numbers together, and all the variables

2x^2+24x-320=0

a = 2; b = 24; c = -320;
Δ = b2-4ac
Δ = 242-4·2·(-320)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-56}{2*2}=\frac{-80}{4}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+56}{2*2}=\frac{32}{4}
=8
$