5x-9=(-4+x)x-3

Solution for 5x-9=(-4+x)x-3 equation:

5x-9=(-4+x)x-3

We move all terms to the left:

5x-9-((-4+x)x-3)=0

We add all the numbers together, and all the variables

5x-((x-4)x-3)-9=0


We calculate terms in parentheses: -((x-4)x-3), so:

(x-4)x-3

We multiply parentheses

x^2-4x-3

Back to the equation:

-(x^2-4x-3)


We get rid of parentheses

-x^2+5x+4x+3-9=0

We add all the numbers together, and all the variables

-1x^2+9x-6=0

a = -1; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-1)·(-6)
Δ = 57
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{-(9)-\sqrt{57}}{2*-1}=\frac{-9-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*-1}=\frac{-9+\sqrt{57}}{-2}
$