5x^2+21x=13

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

5x^2+21x=13

We move all terms to the left:

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

a = 5; b = 21; c = -13;
Δ = b2-4ac
Δ = 212-4·5·(-13)
Δ = 701
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{-(21)-\sqrt{701}}{2*5}=\frac{-21-\sqrt{701}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{701}}{2*5}=\frac{-21+\sqrt{701}}{10}
$