15x-10=6x-(x+2)(-x+3)

Solution for 15x-10=6x-(x+2)(-x+3) equation:

15x-10=6x-(x+2)(-x+3)

We move all terms to the left:

15x-10-(6x-(x+2)(-x+3))=0

We add all the numbers together, and all the variables

15x-(6x-(x+2)(-1x+3))-10=0

We multiply parentheses ..

-(6x-(-1x^2+3x-2x+6))+15x-10=0


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

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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+5x-6

Back to the equation:

-(x^2+5x-6)


We add all the numbers together, and all the variables

15x-(x^2+5x-6)-10=0

We get rid of parentheses

-x^2+15x-5x+6-10=0

We add all the numbers together, and all the variables

-1x^2+10x-4=0

a = -1; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-1)·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*-1}=\frac{-10-2\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*-1}=\frac{-10+2\sqrt{21}}{-2}
$