6x^2+17x=5

Solution for 6x^2+17x=5 equation:

6x^2+17x=5

We move all terms to the left:

6x^2+17x-(5)=0

a = 6; b = 17; c = -5;
Δ = b2-4ac
Δ = 172-4·6·(-5)
Δ = 409
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{409}}{2*6}=\frac{-17-\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{409}}{2*6}=\frac{-17+\sqrt{409}}{12}
$