4x^2+6x+1=5

Solution for 4x^2+6x+1=5 equation:

4x^2+6x+1=5

We move all terms to the left:

4x^2+6x+1-(5)=0

We add all the numbers together, and all the variables

4x^2+6x-4=0

a = 4; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·4·(-4)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*4}=\frac{4}{8}
=1/2
$