3-10x=9-4x(42+6x)

Solution for 3-10x=9-4x(42+6x) equation:

3-10x=9-4x(42+6x)

We move all terms to the left:

3-10x-(9-4x(42+6x))=0

We add all the numbers together, and all the variables

-10x-(9-4x(6x+42))+3=0


We calculate terms in parentheses: -(9-4x(6x+42)), so:

9-4x(6x+42)

determiningTheFunctionDomain
-4x(6x+42)+9

We multiply parentheses

-24x^2-168x+9

Back to the equation:

-(-24x^2-168x+9)


We get rid of parentheses

24x^2+168x-10x-9+3=0

We add all the numbers together, and all the variables

24x^2+158x-6=0

a = 24; b = 158; c = -6;
Δ = b2-4ac
Δ = 1582-4·24·(-6)
Δ = 25540
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:

$\sqrt{\Delta}=\sqrt{25540}=\sqrt{4*6385}=\sqrt{4}*\sqrt{6385}=2\sqrt{6385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(158)-2\sqrt{6385}}{2*24}=\frac{-158-2\sqrt{6385}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(158)+2\sqrt{6385}}{2*24}=\frac{-158+2\sqrt{6385}}{48}
$