15x2+6x=45

Solution for 15x2+6x=45 equation:

15x^2+6x=45

We move all terms to the left:

15x^2+6x-(45)=0

a = 15; b = 6; c = -45;
Δ = b2-4ac
Δ = 62-4·15·(-45)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{19}}{2*15}=\frac{-6-12\sqrt{19}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{19}}{2*15}=\frac{-6+12\sqrt{19}}{30}
$