8x-8=6x-5+2x(x-1.5)

Solution for 8x-8=6x-5+2x(x-1.5) equation:

8x-8=6x-5+2x(x-1.5)

We move all terms to the left:

8x-8-(6x-5+2x(x-1.5))=0


We calculate terms in parentheses: -(6x-5+2x(x-1.5)), so:

6x-5+2x(x-1.5)

determiningTheFunctionDomain
6x+2x(x-1.5)-5

We multiply parentheses

2x^2+6x-3x-5

We add all the numbers together, and all the variables

2x^2+3x-5

Back to the equation:

-(2x^2+3x-5)


We get rid of parentheses

-2x^2+8x-3x+5-8=0

We add all the numbers together, and all the variables

-2x^2+5x-3=0

a = -2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-2)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-2}=\frac{-4}{-4}
=1
$