3x^2+17x+24=5

Solution for 3x^2+17x+24=5 equation:

3x^2+17x+24=5

We move all terms to the left:

3x^2+17x+24-(5)=0

We add all the numbers together, and all the variables

3x^2+17x+19=0

a = 3; b = 17; c = +19;
Δ = b2-4ac
Δ = 172-4·3·19
Δ = 61
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{-(17)-\sqrt{61}}{2*3}=\frac{-17-\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{61}}{2*3}=\frac{-17+\sqrt{61}}{6}
$