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

Solution for (2x-7)+(4-3x)(x+3)=0 equation:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(-3x^2-9x+4x+12)+2x-7=0

We get rid of parentheses

-3x^2-9x+4x+2x+12-7=0

We add all the numbers together, and all the variables

-3x^2-3x+5=0

a = -3; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-3)·5
Δ = 69
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{-(-3)-\sqrt{69}}{2*-3}=\frac{3-\sqrt{69}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*-3}=\frac{3+\sqrt{69}}{-6}
$