(x-7)(7x+2)=(X-7)(8x-3)

Solution for (x-7)(7x+2)=(X-7)(8x-3) equation:

(x-7)(7x+2)=(x-7)(8x-3)

We move all terms to the left:

(x-7)(7x+2)-((x-7)(8x-3))=0

We multiply parentheses ..

(+7x^2+2x-49x-14)-((x-7)(8x-3))=0


We calculate terms in parentheses: -((x-7)(8x-3)), so:

(x-7)(8x-3)

We multiply parentheses ..

(+8x^2-3x-56x+21)

We get rid of parentheses

8x^2-3x-56x+21

We add all the numbers together, and all the variables

8x^2-59x+21

Back to the equation:

-(8x^2-59x+21)


We get rid of parentheses

7x^2-8x^2+2x-49x+59x-14-21=0

We add all the numbers together, and all the variables

-1x^2+12x-35=0

a = -1; b = 12; c = -35;
Δ = b2-4ac
Δ = 122-4·(-1)·(-35)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*-1}=\frac{-10}{-2}
=+5
$