X(2x+3)=65^2

Solution for X(2x+3)=65^2 equation:

X(2X+3)=65^2

We move all terms to the left:

X(2X+3)-(65^2)=0

We add all the numbers together, and all the variables

X(2X+3)-4225=0

We multiply parentheses

2X^2+3X-4225=0

a = 2; b = 3; c = -4225;
Δ = b2-4ac
Δ = 32-4·2·(-4225)
Δ = 33809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{33809}}{2*2}=\frac{-3-\sqrt{33809}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33809}}{2*2}=\frac{-3+\sqrt{33809}}{4}
$