2x-12=5(x-4)2x-12=5(x-4)

Solution for 2x-12=5(x-4)2x-12=5(x-4) equation:

2x-12=5(x-4)2x-12=5(x-4)

We move all terms to the left:

2x-12-(5(x-4)2x-12)=0


We calculate terms in parentheses: -(5(x-4)2x-12), so:

5(x-4)2x-12

We multiply parentheses

10x^2-40x-12

Back to the equation:

-(10x^2-40x-12)


We get rid of parentheses

-10x^2+2x+40x+12-12=0

We add all the numbers together, and all the variables

-10x^2+42x=0

a = -10; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-10)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-10}=\frac{-84}{-20}
=4+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-10}=\frac{0}{-20}
=0
$