(x-2)5x-20=3(x-4)

Solution for (x-2)5x-20=3(x-4) equation:

(x-2)5x-20=3(x-4)

We move all terms to the left:

(x-2)5x-20-(3(x-4))=0

We multiply parentheses

5x^2-10x-(3(x-4))-20=0


We calculate terms in parentheses: -(3(x-4)), so:

3(x-4)

We multiply parentheses

3x-12

Back to the equation:

-(3x-12)


We get rid of parentheses

5x^2-10x-3x+12-20=0

We add all the numbers together, and all the variables

5x^2-13x-8=0

a = 5; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·5·(-8)
Δ = 329
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{-(-13)-\sqrt{329}}{2*5}=\frac{13-\sqrt{329}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{329}}{2*5}=\frac{13+\sqrt{329}}{10}
$