(-x+7)(2x-1)=-(-x+3)(-x+7)

Solution for (-x+7)(2x-1)=-(-x+3)(-x+7) equation:

(-x+7)(2x-1)=-(-x+3)(-x+7)

We move all terms to the left:

(-x+7)(2x-1)-(-(-x+3)(-x+7))=0

We add all the numbers together, and all the variables

(-1x+7)(2x-1)-(-(-1x+3)(-1x+7))=0

We multiply parentheses ..

(-2x^2+x+14x-7)-(-(-1x+3)(-1x+7))=0


We calculate terms in parentheses: -(-(-1x+3)(-1x+7)), so:

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

We multiply parentheses ..

-(+x^2-7x-3x+21)

We get rid of parentheses

-x^2+7x+3x-21

We add all the numbers together, and all the variables

-1x^2+10x-21

Back to the equation:

-(-1x^2+10x-21)


We get rid of parentheses

-2x^2+1x^2+x+14x-10x-7+21=0

We add all the numbers together, and all the variables

-1x^2+5x+14=0

a = -1; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-1)·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-1}=\frac{4}{-2}
=-2
$