13x^2+21x=5-6x

Solution for 13x^2+21x=5-6x equation:

13x^2+21x=5-6x

We move all terms to the left:

13x^2+21x-(5-6x)=0

We add all the numbers together, and all the variables

13x^2+21x-(-6x+5)=0

We get rid of parentheses

13x^2+21x+6x-5=0

We add all the numbers together, and all the variables

13x^2+27x-5=0

a = 13; b = 27; c = -5;
Δ = b2-4ac
Δ = 272-4·13·(-5)
Δ = 989
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{989}}{2*13}=\frac{-27-\sqrt{989}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{989}}{2*13}=\frac{-27+\sqrt{989}}{26}
$