4t^2+4t+1=144

Solution for 4t^2+4t+1=144 equation:

4t^2+4t+1=144

We move all terms to the left:

4t^2+4t+1-(144)=0

We add all the numbers together, and all the variables

4t^2+4t-143=0

a = 4; b = 4; c = -143;
Δ = b2-4ac
Δ = 42-4·4·(-143)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-48}{2*4}=\frac{-52}{8}
=-6+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+48}{2*4}=\frac{44}{8}
=5+1/2
$