X(2x-5)=65

Solution for X(2x-5)=65 equation:

X(2X-5)=65

We move all terms to the left:

X(2X-5)-(65)=0

We multiply parentheses

2X^2-5X-65=0

a = 2; b = -5; c = -65;
Δ = b2-4ac
Δ = -52-4·2·(-65)
Δ = 545
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{-(-5)-\sqrt{545}}{2*2}=\frac{5-\sqrt{545}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{545}}{2*2}=\frac{5+\sqrt{545}}{4}
$