8-(x-1)(3-x)=4(x-1)

Solution for 8-(x-1)(3-x)=4(x-1) equation:

8-(x-1)(3-x)=4(x-1)

We move all terms to the left:

8-(x-1)(3-x)-(4(x-1))=0

We add all the numbers together, and all the variables

-(x-1)(-1x+3)-(4(x-1))+8=0

We multiply parentheses ..

-(-1x^2+3x+x-3)-(4(x-1))+8=0


We calculate terms in parentheses: -(4(x-1)), so:

4(x-1)

We multiply parentheses

4x-4

Back to the equation:

-(4x-4)


We get rid of parentheses

1x^2-3x-x-4x+3+4+8=0

We add all the numbers together, and all the variables

x^2-8x+15=0

a = 1; b = -8; c = +15;
Δ = b2-4ac
Δ = -82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*1}=\frac{10}{2}
=5
$