X(2x-5)=2x+7

Solution for X(2x-5)=2x+7 equation:

X(2X-5)=2X+7

We move all terms to the left:

X(2X-5)-(2X+7)=0

We multiply parentheses

2X^2-5X-(2X+7)=0

We get rid of parentheses

2X^2-5X-2X-7=0

We add all the numbers together, and all the variables

2X^2-7X-7=0

a = 2; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·2·(-7)
Δ = 105
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{-(-7)-\sqrt{105}}{2*2}=\frac{7-\sqrt{105}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{105}}{2*2}=\frac{7+\sqrt{105}}{4}
$