15a^2+17-42=0

Solution for 15a^2+17-42=0 equation:

15a^2+17-42=0

We add all the numbers together, and all the variables

15a^2-25=0

a = 15; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·15·(-25)
Δ = 1500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*15}=\frac{0-10\sqrt{15}}{30}
=-\frac{10\sqrt{15}}{30}
=-\frac{\sqrt{15}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*15}=\frac{0+10\sqrt{15}}{30}
=\frac{10\sqrt{15}}{30}
=\frac{\sqrt{15}}{3}
$