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

Solution for 5-(x+2)x-3(x-2)=0 equation:

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-1x^2-5x+11=0

a = -1; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-1)·11
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{-(-5)-\sqrt{69}}{2*-1}=\frac{5-\sqrt{69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{69}}{2*-1}=\frac{5+\sqrt{69}}{-2}
$