7x^2=32

Solution for 7x^2=32 equation:

7x^2=32

We move all terms to the left:

7x^2-(32)=0

a = 7; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·7·(-32)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*7}=\frac{0-8\sqrt{14}}{14}
=-\frac{8\sqrt{14}}{14}
=-\frac{4\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*7}=\frac{0+8\sqrt{14}}{14}
=\frac{8\sqrt{14}}{14}
=\frac{4\sqrt{14}}{7}
$