X*(2x+3)-x=3x+5

Solution for X*(2x+3)-x=3x+5 equation:

X(2X+3)-X=3X+5

We move all terms to the left:

X(2X+3)-X-(3X+5)=0

We add all the numbers together, and all the variables

-1X+X(2X+3)-(3X+5)=0

We multiply parentheses

2X^2-1X+3X-(3X+5)=0

We get rid of parentheses

2X^2-1X+3X-3X-5=0

We add all the numbers together, and all the variables

2X^2-1X-5=0

a = 2; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·2·(-5)
Δ = 41
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{-(-1)-\sqrt{41}}{2*2}=\frac{1-\sqrt{41}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*2}=\frac{1+\sqrt{41}}{4}
$