3x(x-5)=5x-3

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

3x(x-5)=5x-3

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-(5x-3)=0

We get rid of parentheses

3x^2-15x-5x+3=0

We add all the numbers together, and all the variables

3x^2-20x+3=0

a = 3; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·3·3
Δ = 364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{91}}{2*3}=\frac{20-2\sqrt{91}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{91}}{2*3}=\frac{20+2\sqrt{91}}{6}
$