6(x-3)10=x(3x-4)

Solution for 6(x-3)10=x(3x-4) equation:

6(x-3)10=x(3x-4)

We move all terms to the left:

6(x-3)10-(x(3x-4))=0

We multiply parentheses

60x-(x(3x-4))-180=0


We calculate terms in parentheses: -(x(3x-4)), so:

x(3x-4)

We multiply parentheses

3x^2-4x

Back to the equation:

-(3x^2-4x)


We get rid of parentheses

-3x^2+60x+4x-180=0

We add all the numbers together, and all the variables

-3x^2+64x-180=0

a = -3; b = 64; c = -180;
Δ = b2-4ac
Δ = 642-4·(-3)·(-180)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-44}{2*-3}=\frac{-108}{-6}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+44}{2*-3}=\frac{-20}{-6}
=3+1/3
$