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

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

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

We move all terms to the left:

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

We multiply parentheses

7x^2-21x-(2(x-4))=0


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

2(x-4)

We multiply parentheses

2x-8

Back to the equation:

-(2x-8)


We get rid of parentheses

7x^2-21x-2x+8=0

We add all the numbers together, and all the variables

7x^2-23x+8=0

a = 7; b = -23; c = +8;
Δ = b2-4ac
Δ = -232-4·7·8
Δ = 305
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{-(-23)-\sqrt{305}}{2*7}=\frac{23-\sqrt{305}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{305}}{2*7}=\frac{23+\sqrt{305}}{14}
$