X(3+2x)=377

Solution for X(3+2x)=377 equation:

X(3+2X)=377

We move all terms to the left:

X(3+2X)-(377)=0

We add all the numbers together, and all the variables

X(2X+3)-377=0

We multiply parentheses

2X^2+3X-377=0

a = 2; b = 3; c = -377;
Δ = b2-4ac
Δ = 32-4·2·(-377)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-55}{2*2}=\frac{-58}{4}
=-14+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+55}{2*2}=\frac{52}{4}
=13
$