5*7^(2y)=175

Solution for 5*7^(2y)=175 equation:

5*7^(2y)=175

We move all terms to the left:

5*7^(2y)-(175)=0

Wy multiply elements

35y^2-175=0

a = 35; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·35·(-175)
Δ = 24500
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:

$\sqrt{\Delta}=\sqrt{24500}=\sqrt{4900*5}=\sqrt{4900}*\sqrt{5}=70\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{5}}{2*35}=\frac{0-70\sqrt{5}}{70}
=-\frac{70\sqrt{5}}{70}
=-\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{5}}{2*35}=\frac{0+70\sqrt{5}}{70}
=\frac{70\sqrt{5}}{70}
=\sqrt{5}
$