30x-2=(x-1)(x)

Solution for 30x-2=(x-1)(x) equation:

30x-2=(x-1)(x)

We move all terms to the left:

30x-2-((x-1)(x))=0


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

(x-1)x

We multiply parentheses

x^2-1x

Back to the equation:

-(x^2-1x)


We get rid of parentheses

-x^2+30x+1x-2=0

We add all the numbers together, and all the variables

-1x^2+31x-2=0

a = -1; b = 31; c = -2;
Δ = b2-4ac
Δ = 312-4·(-1)·(-2)
Δ = 953
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{-(31)-\sqrt{953}}{2*-1}=\frac{-31-\sqrt{953}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{953}}{2*-1}=\frac{-31+\sqrt{953}}{-2}
$