10y^2-53+15=0

Solution for 10y^2-53+15=0 equation:

10y^2-53+15=0

We add all the numbers together, and all the variables

10y^2-38=0

a = 10; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·10·(-38)
Δ = 1520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{95}}{2*10}=\frac{0-4\sqrt{95}}{20}
=-\frac{4\sqrt{95}}{20}
=-\frac{\sqrt{95}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{95}}{2*10}=\frac{0+4\sqrt{95}}{20}
=\frac{4\sqrt{95}}{20}
=\frac{\sqrt{95}}{5}
$