6x(10-3x)=8

Solution for 6x(10-3x)=8 equation:

6x(10-3x)=8

We move all terms to the left:

6x(10-3x)-(8)=0

We add all the numbers together, and all the variables

6x(-3x+10)-8=0

We multiply parentheses

-18x^2+60x-8=0

a = -18; b = 60; c = -8;
Δ = b2-4ac
Δ = 602-4·(-18)·(-8)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{21}}{2*-18}=\frac{-60-12\sqrt{21}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{21}}{2*-18}=\frac{-60+12\sqrt{21}}{-36}
$