10=x(3x-13)

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

10=x(3x-13)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(3x-13)), so:

x(3x-13)

We multiply parentheses

3x^2-13x

Back to the equation:

-(3x^2-13x)


We get rid of parentheses

-3x^2+13x+10=0

a = -3; b = 13; c = +10;
Δ = b2-4ac
Δ = 132-4·(-3)·10
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*-3}=\frac{4}{-6}
=-2/3
$