3x(2x+3)-x(3x+5)=1

Solution for 3x(2x+3)-x(3x+5)=1 equation:

3x(2x+3)-x(3x+5)=1

We move all terms to the left:

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

We multiply parentheses

6x^2-3x^2+9x-5x-1=0

We add all the numbers together, and all the variables

3x^2+4x-1=0

a = 3; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·3·(-1)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*3}=\frac{-4-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*3}=\frac{-4+2\sqrt{7}}{6}
$