40(x)^2=190

Solution for 40(x)^2=190 equation:

40(x)^2=190

We move all terms to the left:

40(x)^2-(190)=0

a = 40; b = 0; c = -190;
Δ = b2-4ac
Δ = 02-4·40·(-190)
Δ = 30400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30400}=\sqrt{1600*19}=\sqrt{1600}*\sqrt{19}=40\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{19}}{2*40}=\frac{0-40\sqrt{19}}{80}
=-\frac{40\sqrt{19}}{80}
=-\frac{\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{19}}{2*40}=\frac{0+40\sqrt{19}}{80}
=\frac{40\sqrt{19}}{80}
=\frac{\sqrt{19}}{2}
$