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

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

We multiply parentheses

6x^2-12x+(-1x+3)

We get rid of parentheses

6x^2-12x-1x+3

We add all the numbers together, and all the variables

6x^2-13x+3

Back to the equation:

-(6x^2-13x+3)


We get rid of parentheses

-6x^2+15x+13x-3-10=0

We add all the numbers together, and all the variables

-6x^2+28x-13=0

a = -6; b = 28; c = -13;
Δ = b2-4ac
Δ = 282-4·(-6)·(-13)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{118}}{2*-6}=\frac{-28-2\sqrt{118}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{118}}{2*-6}=\frac{-28+2\sqrt{118}}{-12}
$