8x(x-6)=5(x-6)

Solution for 8x(x-6)=5(x-6) equation:

8x(x-6)=5(x-6)

We move all terms to the left:

8x(x-6)-(5(x-6))=0

We multiply parentheses

8x^2-48x-(5(x-6))=0


We calculate terms in parentheses: -(5(x-6)), so:

5(x-6)

We multiply parentheses

5x-30

Back to the equation:

-(5x-30)


We get rid of parentheses

8x^2-48x-5x+30=0

We add all the numbers together, and all the variables

8x^2-53x+30=0

a = 8; b = -53; c = +30;
Δ = b2-4ac
Δ = -532-4·8·30
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-43}{2*8}=\frac{10}{16}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+43}{2*8}=\frac{96}{16}
=6
$