3(x-7)x=2x-21

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

3(x-7)x=2x-21

We move all terms to the left:

3(x-7)x-(2x-21)=0

We multiply parentheses

3x^2-21x-(2x-21)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-23x+21=0

a = 3; b = -23; c = +21;
Δ = b2-4ac
Δ = -232-4·3·21
Δ = 277
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{277}}{2*3}=\frac{23-\sqrt{277}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{277}}{2*3}=\frac{23+\sqrt{277}}{6}
$