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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -((x^2-3x)), so:

(x^2-3x)

We get rid of parentheses

x^2-3x

Back to the equation:

-(x^2-3x)


We get rid of parentheses

-x^2+5x+3x-1=0

We add all the numbers together, and all the variables

-1x^2+8x-1=0

a = -1; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-1)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{15}}{2*-1}=\frac{-8-2\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{15}}{2*-1}=\frac{-8+2\sqrt{15}}{-2}
$