13x2-x+5=-2x2+11

Solution for 13x2-x+5=-2x2+11 equation:

13x^2-x+5=-2x^2+11

We move all terms to the left:

13x^2-x+5-(-2x^2+11)=0

We add all the numbers together, and all the variables

13x^2-(-2x^2+11)-1x+5=0

We get rid of parentheses

13x^2+2x^2-1x-11+5=0

We add all the numbers together, and all the variables

15x^2-1x-6=0

a = 15; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·15·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*15}=\frac{-18}{30}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*15}=\frac{20}{30}
=2/3
$