3x(2x-7)=4(3x-8)

Solution for 3x(2x-7)=4(3x-8) equation:

3x(2x-7)=4(3x-8)

We move all terms to the left:

3x(2x-7)-(4(3x-8))=0

We multiply parentheses

6x^2-21x-(4(3x-8))=0


We calculate terms in parentheses: -(4(3x-8)), so:

4(3x-8)

We multiply parentheses

12x-32

Back to the equation:

-(12x-32)


We get rid of parentheses

6x^2-21x-12x+32=0

We add all the numbers together, and all the variables

6x^2-33x+32=0

a = 6; b = -33; c = +32;
Δ = b2-4ac
Δ = -332-4·6·32
Δ = 321
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{-(-33)-\sqrt{321}}{2*6}=\frac{33-\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{321}}{2*6}=\frac{33+\sqrt{321}}{12}
$