12x^2=13x=5x

Solution for 12x^2=13x=5x equation:

12x^2=13x=5x

We move all terms to the left:

12x^2-(13x)=0

a = 12; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·12·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*12}=\frac{26}{24}
=1+1/12
$