(5x-3)(18-2x)=(12-x)

Solution for (5x-3)(18-2x)=(12-x) equation:

(5x-3)(18-2x)=(12-x)

We move all terms to the left:

(5x-3)(18-2x)-((12-x))=0

We add all the numbers together, and all the variables

(5x-3)(-2x+18)-((-1x+12))=0

We multiply parentheses ..

(-10x^2+90x+6x-54)-((-1x+12))=0


We calculate terms in parentheses: -((-1x+12)), so:

(-1x+12)

We get rid of parentheses

-1x+12

Back to the equation:

-(-1x+12)


We get rid of parentheses

-10x^2+90x+6x+1x-54-12=0

We add all the numbers together, and all the variables

-10x^2+97x-66=0

a = -10; b = 97; c = -66;
Δ = b2-4ac
Δ = 972-4·(-10)·(-66)
Δ = 6769
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{-(97)-\sqrt{6769}}{2*-10}=\frac{-97-\sqrt{6769}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+\sqrt{6769}}{2*-10}=\frac{-97+\sqrt{6769}}{-20}
$