3*(x-6)=2x(x-7)

Solution for 3*(x-6)=2x(x-7) equation:

3*(x-6)=2x(x-7)

We move all terms to the left:

3*(x-6)-(2x(x-7))=0

We multiply parentheses

3x-(2x(x-7))-18=0


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

2x(x-7)

We multiply parentheses

2x^2-14x

Back to the equation:

-(2x^2-14x)


We get rid of parentheses

-2x^2+3x+14x-18=0

We add all the numbers together, and all the variables

-2x^2+17x-18=0

a = -2; b = 17; c = -18;
Δ = b2-4ac
Δ = 172-4·(-2)·(-18)
Δ = 145
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{-(17)-\sqrt{145}}{2*-2}=\frac{-17-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{145}}{2*-2}=\frac{-17+\sqrt{145}}{-4}
$