(-7x+2)(x+1)=-5(-7x+2)

Solution for (-7x+2)(x+1)=-5(-7x+2) equation:

(-7x+2)(x+1)=-5(-7x+2)

We move all terms to the left:

(-7x+2)(x+1)-(-5(-7x+2))=0

We multiply parentheses ..

(-7x^2-7x+2x+2)-(-5(-7x+2))=0


We calculate terms in parentheses: -(-5(-7x+2)), so:

-5(-7x+2)

We multiply parentheses

35x-10

Back to the equation:

-(35x-10)


We get rid of parentheses

-7x^2-7x+2x-35x+2+10=0

We add all the numbers together, and all the variables

-7x^2-40x+12=0

a = -7; b = -40; c = +12;
Δ = b2-4ac
Δ = -402-4·(-7)·12
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-44}{2*-7}=\frac{-4}{-14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+44}{2*-7}=\frac{84}{-14}
=-6
$