2x^2-23x+4x^2=13

Solution for 2x^2-23x+4x^2=13 equation:

2x^2-23x+4x^2=13

We move all terms to the left:

2x^2-23x+4x^2-(13)=0

We add all the numbers together, and all the variables

6x^2-23x-13=0

a = 6; b = -23; c = -13;
Δ = b2-4ac
Δ = -232-4·6·(-13)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-29}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+29}{2*6}=\frac{52}{12}
=4+1/3
$