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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-(5(x-8)x)-30=0


We calculate terms in parentheses: -(5(x-8)x), so:

5(x-8)x

We multiply parentheses

5x^2-40x

Back to the equation:

-(5x^2-40x)


We get rid of parentheses

-5x^2+5x+40x-30=0

We add all the numbers together, and all the variables

-5x^2+45x-30=0

a = -5; b = 45; c = -30;
Δ = b2-4ac
Δ = 452-4·(-5)·(-30)
Δ = 1425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{57}}{2*-5}=\frac{-45-5\sqrt{57}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{57}}{2*-5}=\frac{-45+5\sqrt{57}}{-10}
$