7Y(5x2)=31

Solution for 7Y(5x2)=31 equation:

7(5Y^2)=31

We move all terms to the left:

7(5Y^2)-(31)=0

a = 75; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·75·(-31)
Δ = 9300
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:

$\sqrt{\Delta}=\sqrt{9300}=\sqrt{100*93}=\sqrt{100}*\sqrt{93}=10\sqrt{93}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{93}}{2*75}=\frac{0-10\sqrt{93}}{150}
=-\frac{10\sqrt{93}}{150}
=-\frac{\sqrt{93}}{15}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{93}}{2*75}=\frac{0+10\sqrt{93}}{150}
=\frac{10\sqrt{93}}{150}
=\frac{\sqrt{93}}{15}
$