5x2-13x=-6

Solution for 5x2-13x=-6 equation:

5x^2-13x=-6

We move all terms to the left:

5x^2-13x-(-6)=0

We add all the numbers together, and all the variables

5x^2-13x+6=0

a = 5; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·5·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*5}=\frac{6}{10}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*5}=\frac{20}{10}
=2
$