6x(10-3x)=18

Solution for 6x(10-3x)=18 equation:

6x(10-3x)=18

We move all terms to the left:

6x(10-3x)-(18)=0

We add all the numbers together, and all the variables

6x(-3x+10)-18=0

We multiply parentheses

-18x^2+60x-18=0

a = -18; b = 60; c = -18;
Δ = b2-4ac
Δ = 602-4·(-18)·(-18)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-48}{2*-18}=\frac{-108}{-36}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+48}{2*-18}=\frac{-12}{-36}
=1/3
$