-4(x-2)=-2x(x-8.5)

Solution for -4(x-2)=-2x(x-8.5) equation:

-4(x-2)=-2x(x-8.5)

We move all terms to the left:

-4(x-2)-(-2x(x-8.5))=0

We multiply parentheses

-4x-(-2x(x-8.5))+8=0


We calculate terms in parentheses: -(-2x(x-8.5)), so:

-2x(x-8.5)

We multiply parentheses

-2x^2+17x

Back to the equation:

-(-2x^2+17x)


We get rid of parentheses

2x^2-17x-4x+8=0

We add all the numbers together, and all the variables

2x^2-21x+8=0

a = 2; b = -21; c = +8;
Δ = b2-4ac
Δ = -212-4·2·8
Δ = 377
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{377}}{2*2}=\frac{21-\sqrt{377}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{377}}{2*2}=\frac{21+\sqrt{377}}{4}
$