-6(x-5)33x=6x-10(-3+x)

Solution for -6(x-5)33x=6x-10(-3+x) equation:

-6(x-5)33x=6x-10(-3+x)

We move all terms to the left:

-6(x-5)33x-(6x-10(-3+x))=0

We add all the numbers together, and all the variables

-6(x-5)33x-(6x-10(x-3))=0

We multiply parentheses

-198x^2+990x-(6x-10(x-3))=0


We calculate terms in parentheses: -(6x-10(x-3)), so:

6x-10(x-3)

We multiply parentheses

6x-10x+30

We add all the numbers together, and all the variables

-4x+30

Back to the equation:

-(-4x+30)


We get rid of parentheses

-198x^2+990x+4x-30=0

We add all the numbers together, and all the variables

-198x^2+994x-30=0

a = -198; b = 994; c = -30;
Δ = b2-4ac
Δ = 9942-4·(-198)·(-30)
Δ = 964276
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:

$\sqrt{\Delta}=\sqrt{964276}=\sqrt{4*241069}=\sqrt{4}*\sqrt{241069}=2\sqrt{241069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(994)-2\sqrt{241069}}{2*-198}=\frac{-994-2\sqrt{241069}}{-396}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(994)+2\sqrt{241069}}{2*-198}=\frac{-994+2\sqrt{241069}}{-396}
$