5x-6=x(x-10)

Solution for 5x-6=x(x-10) equation:

5x-6=x(x-10)

We move all terms to the left:

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


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

x(x-10)

We multiply parentheses

x^2-10x

Back to the equation:

-(x^2-10x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+15x-6=0

a = -1; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-1)·(-6)
Δ = 201
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{-(15)-\sqrt{201}}{2*-1}=\frac{-15-\sqrt{201}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*-1}=\frac{-15+\sqrt{201}}{-2}
$