40x^2+30-135=0

Solution for 40x^2+30-135=0 equation:

40x^2+30-135=0

We add all the numbers together, and all the variables

40x^2-105=0

a = 40; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·40·(-105)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{42}}{2*40}=\frac{0-20\sqrt{42}}{80}
=-\frac{20\sqrt{42}}{80}
=-\frac{\sqrt{42}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{42}}{2*40}=\frac{0+20\sqrt{42}}{80}
=\frac{20\sqrt{42}}{80}
=\frac{\sqrt{42}}{4}
$