2x^2-15x-27x=-3

Solution for 2x^2-15x-27x=-3 equation:

2x^2-15x-27x=-3

We move all terms to the left:

2x^2-15x-27x-(-3)=0

We add all the numbers together, and all the variables

2x^2-42x+3=0

a = 2; b = -42; c = +3;
Δ = b2-4ac
Δ = -422-4·2·3
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*2}=\frac{42-2\sqrt{435}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*2}=\frac{42+2\sqrt{435}}{4}
$