3x(x-3)=5(2x-1)

Solution for 3x(x-3)=5(2x-1) equation:

3x(x-3)=5(2x-1)

We move all terms to the left:

3x(x-3)-(5(2x-1))=0

We multiply parentheses

3x^2-9x-(5(2x-1))=0


We calculate terms in parentheses: -(5(2x-1)), so:

5(2x-1)

We multiply parentheses

10x-5

Back to the equation:

-(10x-5)


We get rid of parentheses

3x^2-9x-10x+5=0

We add all the numbers together, and all the variables

3x^2-19x+5=0

a = 3; b = -19; c = +5;
Δ = b2-4ac
Δ = -192-4·3·5
Δ = 301
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{-(-19)-\sqrt{301}}{2*3}=\frac{19-\sqrt{301}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{301}}{2*3}=\frac{19+\sqrt{301}}{6}
$