6x-3(3x-4)=2x(x-7)-4

Solution for 6x-3(3x-4)=2x(x-7)-4 equation:

6x-3(3x-4)=2x(x-7)-4

We move all terms to the left:

6x-3(3x-4)-(2x(x-7)-4)=0

We multiply parentheses

6x-9x-(2x(x-7)-4)+12=0


We calculate terms in parentheses: -(2x(x-7)-4), so:

2x(x-7)-4

We multiply parentheses

2x^2-14x-4

Back to the equation:

-(2x^2-14x-4)


We add all the numbers together, and all the variables

-3x-(2x^2-14x-4)+12=0

We get rid of parentheses

-2x^2-3x+14x+4+12=0

We add all the numbers together, and all the variables

-2x^2+11x+16=0

a = -2; b = 11; c = +16;
Δ = b2-4ac
Δ = 112-4·(-2)·16
Δ = 249
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{-(11)-\sqrt{249}}{2*-2}=\frac{-11-\sqrt{249}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{249}}{2*-2}=\frac{-11+\sqrt{249}}{-4}
$