3x(2x+5)-4(x+3)=2x+3

Solution for 3x(2x+5)-4(x+3)=2x+3 equation:

3x(2x+5)-4(x+3)=2x+3

We move all terms to the left:

3x(2x+5)-4(x+3)-(2x+3)=0

We multiply parentheses

6x^2+15x-4x-(2x+3)-12=0

We get rid of parentheses

6x^2+15x-4x-2x-3-12=0

We add all the numbers together, and all the variables

6x^2+9x-15=0

a = 6; b = 9; c = -15;
Δ = b2-4ac
Δ = 92-4·6·(-15)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*6}=\frac{12}{12}
=1
$