2x(x-3)-7=18-5(x-4)

Solution for 2x(x-3)-7=18-5(x-4) equation:

2x(x-3)-7=18-5(x-4)

We move all terms to the left:

2x(x-3)-7-(18-5(x-4))=0

We multiply parentheses

2x^2-6x-(18-5(x-4))-7=0


We calculate terms in parentheses: -(18-5(x-4)), so:

18-5(x-4)

determiningTheFunctionDomain
-5(x-4)+18

We multiply parentheses

-5x+20+18

We add all the numbers together, and all the variables

-5x+38

Back to the equation:

-(-5x+38)


We get rid of parentheses

2x^2-6x+5x-38-7=0

We add all the numbers together, and all the variables

2x^2-1x-45=0

a = 2; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·2·(-45)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*2}=\frac{-18}{4}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*2}=\frac{20}{4}
=5
$