10x(x-1)=6(x+3)

Solution for 10x(x-1)=6(x+3) equation:

10x(x-1)=6(x+3)

We move all terms to the left:

10x(x-1)-(6(x+3))=0

We multiply parentheses

10x^2-10x-(6(x+3))=0


We calculate terms in parentheses: -(6(x+3)), so:

6(x+3)

We multiply parentheses

6x+18

Back to the equation:

-(6x+18)


We get rid of parentheses

10x^2-10x-6x-18=0

We add all the numbers together, and all the variables

10x^2-16x-18=0

a = 10; b = -16; c = -18;
Δ = b2-4ac
Δ = -162-4·10·(-18)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{61}}{2*10}=\frac{16-4\sqrt{61}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{61}}{2*10}=\frac{16+4\sqrt{61}}{20}
$