1000=4x^2+10

Solution for 1000=4x^2+10 equation:

1000=4x^2+10

We move all terms to the left:

1000-(4x^2+10)=0

We get rid of parentheses

-4x^2-10+1000=0

We add all the numbers together, and all the variables

-4x^2+990=0

a = -4; b = 0; c = +990;
Δ = b2-4ac
Δ = 02-4·(-4)·990
Δ = 15840
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:

$\sqrt{\Delta}=\sqrt{15840}=\sqrt{144*110}=\sqrt{144}*\sqrt{110}=12\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{110}}{2*-4}=\frac{0-12\sqrt{110}}{-8}
=-\frac{12\sqrt{110}}{-8}
=-\frac{3\sqrt{110}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{110}}{2*-4}=\frac{0+12\sqrt{110}}{-8}
=\frac{12\sqrt{110}}{-8}
=\frac{3\sqrt{110}}{-2}
$