10x^2-7=583

Solution for 10x^2-7=583 equation:

10x^2-7=583

We move all terms to the left:

10x^2-7-(583)=0

We add all the numbers together, and all the variables

10x^2-590=0

a = 10; b = 0; c = -590;
Δ = b2-4ac
Δ = 02-4·10·(-590)
Δ = 23600
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:

$\sqrt{\Delta}=\sqrt{23600}=\sqrt{400*59}=\sqrt{400}*\sqrt{59}=20\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{59}}{2*10}=\frac{0-20\sqrt{59}}{20}
=-\frac{20\sqrt{59}}{20}
=-\sqrt{59}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{59}}{2*10}=\frac{0+20\sqrt{59}}{20}
=\frac{20\sqrt{59}}{20}
=\sqrt{59}
$