9u^2-15=75

Solution for 9u^2-15=75 equation:

9u^2-15=75

We move all terms to the left:

9u^2-15-(75)=0

We add all the numbers together, and all the variables

9u^2-90=0

a = 9; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·9·(-90)
Δ = 3240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{10}}{2*9}=\frac{0-18\sqrt{10}}{18}
=-\frac{18\sqrt{10}}{18}
=-\sqrt{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{10}}{2*9}=\frac{0+18\sqrt{10}}{18}
=\frac{18\sqrt{10}}{18}
=\sqrt{10}
$