5+x=3x(x-7)+6

Solution for 5+x=3x(x-7)+6 equation:

5+x=3x(x-7)+6

We move all terms to the left:

5+x-(3x(x-7)+6)=0


We calculate terms in parentheses: -(3x(x-7)+6), so:

3x(x-7)+6

We multiply parentheses

3x^2-21x+6

Back to the equation:

-(3x^2-21x+6)


We get rid of parentheses

-3x^2+x+21x-6+5=0

We add all the numbers together, and all the variables

-3x^2+22x-1=0

a = -3; b = 22; c = -1;
Δ = b2-4ac
Δ = 222-4·(-3)·(-1)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{118}}{2*-3}=\frac{-22-2\sqrt{118}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{118}}{2*-3}=\frac{-22+2\sqrt{118}}{-6}
$