8x-10=3(6-2x)x=

Solution for 8x-10=3(6-2x)x= equation:

8x-10=3(6-2x)x=

We move all terms to the left:

8x-10-(3(6-2x)x)=0

We add all the numbers together, and all the variables

8x-(3(-2x+6)x)-10=0


We calculate terms in parentheses: -(3(-2x+6)x), so:

3(-2x+6)x

We multiply parentheses

-6x^2+18x

Back to the equation:

-(-6x^2+18x)


We get rid of parentheses

6x^2-18x+8x-10=0

We add all the numbers together, and all the variables

6x^2-10x-10=0

a = 6; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·6·(-10)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*6}=\frac{10-2\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*6}=\frac{10+2\sqrt{85}}{12}
$