5x^2-+34x=-24

Solution for 5x^2-+34x=-24 equation:

5x^2-+34x=-24

We move all terms to the left:

5x^2-+34x-(-24)=0

We add all the numbers together, and all the variables

5x^2+34x-24=0

a = 5; b = 34; c = -24;
Δ = b2-4ac
Δ = 342-4·5·(-24)
Δ = 1636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{409}}{2*5}=\frac{-34-2\sqrt{409}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{409}}{2*5}=\frac{-34+2\sqrt{409}}{10}
$