x(2x-13)=-6

Solution for x(2x-13)=-6 equation:

x(2x-13)=-6

We move all terms to the left:

x(2x-13)-(-6)=0

We add all the numbers together, and all the variables

x(2x-13)+6=0

We multiply parentheses

2x^2-13x+6=0

a = 2; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·2·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*2}=\frac{24}{4}
=6
$