4x^2-7=193

Solution for 4x^2-7=193 equation:

4x^2-7=193

We move all terms to the left:

4x^2-7-(193)=0

We add all the numbers together, and all the variables

4x^2-200=0

a = 4; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·4·(-200)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*4}=\frac{0-40\sqrt{2}}{8}
=-\frac{40\sqrt{2}}{8}
=-5\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*4}=\frac{0+40\sqrt{2}}{8}
=\frac{40\sqrt{2}}{8}
=5\sqrt{2}
$