4x^2+1=75-4x

Solution for 4x^2+1=75-4x equation:

4x^2+1=75-4x

We move all terms to the left:

4x^2+1-(75-4x)=0

We add all the numbers together, and all the variables

4x^2-(-4x+75)+1=0

We get rid of parentheses

4x^2+4x-75+1=0

We add all the numbers together, and all the variables

4x^2+4x-74=0

a = 4; b = 4; c = -74;
Δ = b2-4ac
Δ = 42-4·4·(-74)
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{-(4)-20\sqrt{3}}{2*4}=\frac{-4-20\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20\sqrt{3}}{2*4}=\frac{-4+20\sqrt{3}}{8}
$