-3(x-1)+8=6x+7-5x(x-3)

Solution for -3(x-1)+8=6x+7-5x(x-3) equation:

-3(x-1)+8=6x+7-5x(x-3)

We move all terms to the left:

-3(x-1)+8-(6x+7-5x(x-3))=0

We multiply parentheses

-3x-(6x+7-5x(x-3))+3+8=0


We calculate terms in parentheses: -(6x+7-5x(x-3)), so:

6x+7-5x(x-3)

determiningTheFunctionDomain
6x-5x(x-3)+7

We multiply parentheses

-5x^2+6x+15x+7

We add all the numbers together, and all the variables

-5x^2+21x+7

Back to the equation:

-(-5x^2+21x+7)


We add all the numbers together, and all the variables

-(-5x^2+21x+7)-3x+11=0

We get rid of parentheses

5x^2-21x-3x-7+11=0

We add all the numbers together, and all the variables

5x^2-24x+4=0

a = 5; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·5·4
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{31}}{2*5}=\frac{24-4\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{31}}{2*5}=\frac{24+4\sqrt{31}}{10}
$