15=(2x-1)(x-3)

Solution for 15=(2x-1)(x-3) equation:

15=(2x-1)(x-3)

We move all terms to the left:

15-((2x-1)(x-3))=0

We multiply parentheses ..

-((+2x^2-6x-1x+3))+15=0


We calculate terms in parentheses: -((+2x^2-6x-1x+3)), so:

(+2x^2-6x-1x+3)

We get rid of parentheses

2x^2-6x-1x+3

We add all the numbers together, and all the variables

2x^2-7x+3

Back to the equation:

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


We get rid of parentheses

-2x^2+7x-3+15=0

We add all the numbers together, and all the variables

-2x^2+7x+12=0

a = -2; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-2)·12
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*-2}=\frac{-7-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*-2}=\frac{-7+\sqrt{145}}{-4}
$