5x(x-1)=5x*2-(8-3x)

Solution for 5x(x-1)=5x*2-(8-3x) equation:

5x(x-1)=5x*2-(8-3x)

We move all terms to the left:

5x(x-1)-(5x*2-(8-3x))=0

We add all the numbers together, and all the variables

5x(x-1)-(5x*2-(-3x+8))=0

We multiply parentheses

5x^2-5x-(5x*2-(-3x+8))=0


We calculate terms in parentheses: -(5x*2-(-3x+8)), so:

5x*2-(-3x+8)

Wy multiply elements

10x-(-3x+8)

We get rid of parentheses

10x+3x-8

We add all the numbers together, and all the variables

13x-8

Back to the equation:

-(13x-8)


We get rid of parentheses

5x^2-5x-13x+8=0

We add all the numbers together, and all the variables

5x^2-18x+8=0

a = 5; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·5·8
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{41}}{2*5}=\frac{18-2\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{41}}{2*5}=\frac{18+2\sqrt{41}}{10}
$