x(2x+3)-242=3x

Solution for x(2x+3)-242=3x equation:

x(2x+3)-242=3x

We move all terms to the left:

x(2x+3)-242-(3x)=0

We add all the numbers together, and all the variables

-3x+x(2x+3)-242=0

We multiply parentheses

2x^2-3x+3x-242=0

We add all the numbers together, and all the variables

2x^2-242=0

a = 2; b = 0; c = -242;
Δ = b2-4ac
Δ = 02-4·2·(-242)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44}{2*2}=\frac{44}{4}
=11
$