3x+(5-x^2)=5x-8+2x-4

Solution for 3x+(5-x^2)=5x-8+2x-4 equation:

3x+(5-x^2)=5x-8+2x-4

We move all terms to the left:

3x+(5-x^2)-(5x-8+2x-4)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+3x-7x+5+12=0

We add all the numbers together, and all the variables

-1x^2-4x+17=0

a = -1; b = -4; c = +17;
Δ = b2-4ac
Δ = -42-4·(-1)·17
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{21}}{2*-1}=\frac{4-2\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{21}}{2*-1}=\frac{4+2\sqrt{21}}{-2}
$