3x(x+13)=10(x-1)

Solution for 3x(x+13)=10(x-1) equation:

3x(x+13)=10(x-1)

We move all terms to the left:

3x(x+13)-(10(x-1))=0

We multiply parentheses

3x^2+39x-(10(x-1))=0


We calculate terms in parentheses: -(10(x-1)), so:

10(x-1)

We multiply parentheses

10x-10

Back to the equation:

-(10x-10)


We get rid of parentheses

3x^2+39x-10x+10=0

We add all the numbers together, and all the variables

3x^2+29x+10=0

a = 3; b = 29; c = +10;
Δ = b2-4ac
Δ = 292-4·3·10
Δ = 721
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{-(29)-\sqrt{721}}{2*3}=\frac{-29-\sqrt{721}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{721}}{2*3}=\frac{-29+\sqrt{721}}{6}
$