2x-7x-6=x(x-6)-10

Solution for 2x-7x-6=x(x-6)-10 equation:

2x-7x-6=x(x-6)-10

We move all terms to the left:

2x-7x-6-(x(x-6)-10)=0

We add all the numbers together, and all the variables

-5x-(x(x-6)-10)-6=0


We calculate terms in parentheses: -(x(x-6)-10), so:

x(x-6)-10

We multiply parentheses

x^2-6x-10

Back to the equation:

-(x^2-6x-10)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+x+4=0

a = -1; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-1)·4
Δ = 17
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{-(1)-\sqrt{17}}{2*-1}=\frac{-1-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-1}=\frac{-1+\sqrt{17}}{-2}
$