13=3x(x-2)-(x-5)

Solution for 13=3x(x-2)-(x-5) equation:

13=3x(x-2)-(x-5)

We move all terms to the left:

13-(3x(x-2)-(x-5))=0


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

3x(x-2)-(x-5)

We multiply parentheses

3x^2-6x-(x-5)

We get rid of parentheses

3x^2-6x-x+5

We add all the numbers together, and all the variables

3x^2-7x+5

Back to the equation:

-(3x^2-7x+5)


We get rid of parentheses

-3x^2+7x-5+13=0

We add all the numbers together, and all the variables

-3x^2+7x+8=0

a = -3; b = 7; c = +8;
Δ = b2-4ac
Δ = 72-4·(-3)·8
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{145}}{2*-3}=\frac{-7-\sqrt{145}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*-3}=\frac{-7+\sqrt{145}}{-6}
$