4x-5=2+3(x-3)4x-5=2+3(x-3)

Solution for 4x-5=2+3(x-3)4x-5=2+3(x-3) equation:

4x-5=2+3(x-3)4x-5=2+3(x-3)

We move all terms to the left:

4x-5-(2+3(x-3)4x-5)=0


We calculate terms in parentheses: -(2+3(x-3)4x-5), so:

2+3(x-3)4x-5

determiningTheFunctionDomain
3(x-3)4x+2-5

We add all the numbers together, and all the variables

3(x-3)4x-3

We multiply parentheses

12x^2-36x-3

Back to the equation:

-(12x^2-36x-3)


We get rid of parentheses

-12x^2+4x+36x+3-5=0

We add all the numbers together, and all the variables

-12x^2+40x-2=0

a = -12; b = 40; c = -2;
Δ = b2-4ac
Δ = 402-4·(-12)·(-2)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{94}}{2*-12}=\frac{-40-4\sqrt{94}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{94}}{2*-12}=\frac{-40+4\sqrt{94}}{-24}
$