x^2/5-10=-3

Solution for x^2/5-10=-3 equation:

x^2/5-10=-3

We move all terms to the left:

x^2/5-10-(-3)=0

We add all the numbers together, and all the variables

x^2/5-7=0

We multiply all the terms by the denominator


x^2-7*5=0

We add all the numbers together, and all the variables

x^2-35=0

a = 1; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·1·(-35)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*1}=\frac{0-2\sqrt{35}}{2}
=-\frac{2\sqrt{35}}{2}
=-\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*1}=\frac{0+2\sqrt{35}}{2}
=\frac{2\sqrt{35}}{2}
=\sqrt{35}
$