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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+30x^2-40x-30x+40)=0

We get rid of parentheses

30x^2-40x-30x+40=0

We add all the numbers together, and all the variables

30x^2-70x+40=0

a = 30; b = -70; c = +40;
Δ = b2-4ac
Δ = -702-4·30·40
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10}{2*30}=\frac{60}{60}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10}{2*30}=\frac{80}{60}
=1+1/3
$