(3x-1)(4x+4)=(8x+7)(1x+7)

Solution for (3x-1)(4x+4)=(8x+7)(1x+7) equation:

(3x-1)(4x+4)=(8x+7)(1x+7)

We move all terms to the left:

(3x-1)(4x+4)-((8x+7)(1x+7))=0

We add all the numbers together, and all the variables

(3x-1)(4x+4)-((8x+7)(x+7))=0

We multiply parentheses ..

(+12x^2+12x-4x-4)-((8x+7)(x+7))=0


We calculate terms in parentheses: -((8x+7)(x+7)), so:

(8x+7)(x+7)

We multiply parentheses ..

(+8x^2+56x+7x+49)

We get rid of parentheses

8x^2+56x+7x+49

We add all the numbers together, and all the variables

8x^2+63x+49

Back to the equation:

-(8x^2+63x+49)


We get rid of parentheses

12x^2-8x^2+12x-4x-63x-4-49=0

We add all the numbers together, and all the variables

4x^2-55x-53=0

a = 4; b = -55; c = -53;
Δ = b2-4ac
Δ = -552-4·4·(-53)
Δ = 3873
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{-(-55)-\sqrt{3873}}{2*4}=\frac{55-\sqrt{3873}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3873}}{2*4}=\frac{55+\sqrt{3873}}{8}
$