2(x+2)-3x(x-3)=x+7

Solution for 2(x+2)-3x(x-3)=x+7 equation:

2(x+2)-3x(x-3)=x+7

We move all terms to the left:

2(x+2)-3x(x-3)-(x+7)=0

We multiply parentheses

-3x^2+2x+9x-(x+7)+4=0

We get rid of parentheses

-3x^2+2x+9x-x-7+4=0

We add all the numbers together, and all the variables

-3x^2+10x-3=0

a = -3; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-3)·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*-3}=\frac{-2}{-6}
=1/3
$