4x^2+25=100

Solution for 4x^2+25=100 equation:

4x^2+25=100

We move all terms to the left:

4x^2+25-(100)=0

We add all the numbers together, and all the variables

4x^2-75=0

a = 4; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·4·(-75)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*4}=\frac{0-20\sqrt{3}}{8}
=-\frac{20\sqrt{3}}{8}
=-\frac{5\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*4}=\frac{0+20\sqrt{3}}{8}
=\frac{20\sqrt{3}}{8}
=\frac{5\sqrt{3}}{2}
$