3x(x-4)-7=2(x-3)

Solution for 3x(x-4)-7=2(x-3) equation:

3x(x-4)-7=2(x-3)

We move all terms to the left:

3x(x-4)-7-(2(x-3))=0

We multiply parentheses

3x^2-12x-(2(x-3))-7=0


We calculate terms in parentheses: -(2(x-3)), so:

2(x-3)

We multiply parentheses

2x-6

Back to the equation:

-(2x-6)


We get rid of parentheses

3x^2-12x-2x+6-7=0

We add all the numbers together, and all the variables

3x^2-14x-1=0

a = 3; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·3·(-1)
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{13}}{2*3}=\frac{14-4\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{13}}{2*3}=\frac{14+4\sqrt{13}}{6}
$