7-10u^2=-73

Solution for 7-10u^2=-73 equation:

7-10u^2=-73

We move all terms to the left:

7-10u^2-(-73)=0

We add all the numbers together, and all the variables

-10u^2+80=0

a = -10; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-10)·80
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-10}=\frac{0-40\sqrt{2}}{-20}
=-\frac{40\sqrt{2}}{-20}
=-\frac{2\sqrt{2}}{-1}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-10}=\frac{0+40\sqrt{2}}{-20}
=\frac{40\sqrt{2}}{-20}
=\frac{2\sqrt{2}}{-1}
$