10x^2-5=58

Solution for 10x^2-5=58 equation:

10x^2-5=58

We move all terms to the left:

10x^2-5-(58)=0

We add all the numbers together, and all the variables

10x^2-63=0

a = 10; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·10·(-63)
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{70}}{2*10}=\frac{0-6\sqrt{70}}{20}
=-\frac{6\sqrt{70}}{20}
=-\frac{3\sqrt{70}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{70}}{2*10}=\frac{0+6\sqrt{70}}{20}
=\frac{6\sqrt{70}}{20}
=\frac{3\sqrt{70}}{10}
$