(7x-8)(x+7)=(-5x+1)(x-8)

Solution for (7x-8)(x+7)=(-5x+1)(x-8) equation:

(7x-8)(x+7)=(-5x+1)(x-8)

We move all terms to the left:

(7x-8)(x+7)-((-5x+1)(x-8))=0

We multiply parentheses ..

(+7x^2+49x-8x-56)-((-5x+1)(x-8))=0


We calculate terms in parentheses: -((-5x+1)(x-8)), so:

(-5x+1)(x-8)

We multiply parentheses ..

(-5x^2+40x+x-8)

We get rid of parentheses

-5x^2+40x+x-8

We add all the numbers together, and all the variables

-5x^2+41x-8

Back to the equation:

-(-5x^2+41x-8)


We get rid of parentheses

7x^2+5x^2+49x-8x-41x-56+8=0

We add all the numbers together, and all the variables

12x^2-48=0

a = 12; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·12·(-48)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*12}=\frac{48}{24}
=2
$