6x+36x^2=15

Solution for 6x+36x^2=15 equation:

6x+36x^2=15

We move all terms to the left:

6x+36x^2-(15)=0

a = 36; b = 6; c = -15;
Δ = b2-4ac
Δ = 62-4·36·(-15)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{61}}{2*36}=\frac{-6-6\sqrt{61}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{61}}{2*36}=\frac{-6+6\sqrt{61}}{72}
$