6x+7(x-3)=x^2-3x+7x-21

Solution for 6x+7(x-3)=x^2-3x+7x-21 equation:

6x+7(x-3)=x^2-3x+7x-21

We move all terms to the left:

6x+7(x-3)-(x^2-3x+7x-21)=0

We multiply parentheses

6x+7x-(x^2-3x+7x-21)-21=0

We get rid of parentheses

-x^2+6x+7x+3x-7x+21-21=0

We add all the numbers together, and all the variables

-1x^2+9x=0

a = -1; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1)·0
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{-(9)-9}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1}=\frac{0}{-2}
=0
$