x(2x-30)=(x+10)

Solution for x(2x-30)=(x+10) equation:

x(2x-30)=(x+10)

We move all terms to the left:

x(2x-30)-((x+10))=0

We multiply parentheses

2x^2-30x-((x+10))=0


We calculate terms in parentheses: -((x+10)), so:

(x+10)

We get rid of parentheses

x+10

Back to the equation:

-(x+10)


We get rid of parentheses

2x^2-30x-x-10=0

We add all the numbers together, and all the variables

2x^2-31x-10=0

a = 2; b = -31; c = -10;
Δ = b2-4ac
Δ = -312-4·2·(-10)
Δ = 1041
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{1041}}{2*2}=\frac{31-\sqrt{1041}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1041}}{2*2}=\frac{31+\sqrt{1041}}{4}
$