(4x-3)(x-1)=(3x+3)(x-7)

Solution for (4x-3)(x-1)=(3x+3)(x-7) equation:

(4x-3)(x-1)=(3x+3)(x-7)

We move all terms to the left:

(4x-3)(x-1)-((3x+3)(x-7))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((3x+3)(x-7)), so:

(3x+3)(x-7)

We multiply parentheses ..

(+3x^2-21x+3x-21)

We get rid of parentheses

3x^2-21x+3x-21

We add all the numbers together, and all the variables

3x^2-18x-21

Back to the equation:

-(3x^2-18x-21)


We get rid of parentheses

4x^2-3x^2-4x-3x+18x+3+21=0

We add all the numbers together, and all the variables

x^2+11x+24=0

a = 1; b = 11; c = +24;
Δ = b2-4ac
Δ = 112-4·1·24
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*1}=\frac{-6}{2}
=-3
$