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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3(-1x+4)-(7x(x+2)-6)=0

We multiply parentheses

-3x-(7x(x+2)-6)+12=0


We calculate terms in parentheses: -(7x(x+2)-6), so:

7x(x+2)-6

We multiply parentheses

7x^2+14x-6

Back to the equation:

-(7x^2+14x-6)


We get rid of parentheses

-7x^2-3x-14x+6+12=0

We add all the numbers together, and all the variables

-7x^2-17x+18=0

a = -7; b = -17; c = +18;
Δ = b2-4ac
Δ = -172-4·(-7)·18
Δ = 793
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{793}}{2*-7}=\frac{17-\sqrt{793}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{793}}{2*-7}=\frac{17+\sqrt{793}}{-14}
$