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

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

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

We move all terms to the left:

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

We multiply parentheses

-5x^2+50x-(6(x-10))=0


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

6(x-10)

We multiply parentheses

6x-60

Back to the equation:

-(6x-60)


We get rid of parentheses

-5x^2+50x-6x+60=0

We add all the numbers together, and all the variables

-5x^2+44x+60=0

a = -5; b = 44; c = +60;
Δ = b2-4ac
Δ = 442-4·(-5)·60
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-56}{2*-5}=\frac{-100}{-10}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+56}{2*-5}=\frac{12}{-10}
=-1+1/5
$