1x-4=3(x-6)x=

Solution for 1x-4=3(x-6)x= equation:

1x-4=3(x-6)x=

We move all terms to the left:

1x-4-(3(x-6)x)=0

We add all the numbers together, and all the variables

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


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

3(x-6)x

We multiply parentheses

3x^2-18x

Back to the equation:

-(3x^2-18x)


We get rid of parentheses

-3x^2+x+18x-4=0

We add all the numbers together, and all the variables

-3x^2+19x-4=0

a = -3; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·(-3)·(-4)
Δ = 313
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{-(19)-\sqrt{313}}{2*-3}=\frac{-19-\sqrt{313}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{313}}{2*-3}=\frac{-19+\sqrt{313}}{-6}
$