4x+2=(3x-3)(4x-10)

Solution for 4x+2=(3x-3)(4x-10) equation:

4x+2=(3x-3)(4x-10)

We move all terms to the left:

4x+2-((3x-3)(4x-10))=0

We multiply parentheses ..

-((+12x^2-30x-12x+30))+4x+2=0


We calculate terms in parentheses: -((+12x^2-30x-12x+30)), so:

(+12x^2-30x-12x+30)

We get rid of parentheses

12x^2-30x-12x+30

We add all the numbers together, and all the variables

12x^2-42x+30

Back to the equation:

-(12x^2-42x+30)


We add all the numbers together, and all the variables

4x-(12x^2-42x+30)+2=0

We get rid of parentheses

-12x^2+4x+42x-30+2=0

We add all the numbers together, and all the variables

-12x^2+46x-28=0

a = -12; b = 46; c = -28;
Δ = b2-4ac
Δ = 462-4·(-12)·(-28)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{193}}{2*-12}=\frac{-46-2\sqrt{193}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{193}}{2*-12}=\frac{-46+2\sqrt{193}}{-24}
$