38x^2=43

Solution for 38x^2=43 equation:

38x^2=43

We move all terms to the left:

38x^2-(43)=0

a = 38; b = 0; c = -43;
Δ = b2-4ac
Δ = 02-4·38·(-43)
Δ = 6536
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:

$\sqrt{\Delta}=\sqrt{6536}=\sqrt{4*1634}=\sqrt{4}*\sqrt{1634}=2\sqrt{1634}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1634}}{2*38}=\frac{0-2\sqrt{1634}}{76}
=-\frac{2\sqrt{1634}}{76}
=-\frac{\sqrt{1634}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1634}}{2*38}=\frac{0+2\sqrt{1634}}{76}
=\frac{2\sqrt{1634}}{76}
=\frac{\sqrt{1634}}{38}
$