6x(x-1)=18-29x

Solution for 6x(x-1)=18-29x equation:

6x(x-1)=18-29x

We move all terms to the left:

6x(x-1)-(18-29x)=0

We add all the numbers together, and all the variables

6x(x-1)-(-29x+18)=0

We multiply parentheses

6x^2-6x-(-29x+18)=0

We get rid of parentheses

6x^2-6x+29x-18=0

We add all the numbers together, and all the variables

6x^2+23x-18=0

a = 6; b = 23; c = -18;
Δ = b2-4ac
Δ = 232-4·6·(-18)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-31}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+31}{2*6}=\frac{8}{12}
=2/3
$