194x^2+46x+5=144x^2

Solution for 194x^2+46x+5=144x^2 equation:

194x^2+46x+5=144x^2

We move all terms to the left:

194x^2+46x+5-(144x^2)=0

determiningTheFunctionDomain
194x^2-144x^2+46x+5=0

We add all the numbers together, and all the variables

50x^2+46x+5=0

a = 50; b = 46; c = +5;
Δ = b2-4ac
Δ = 462-4·50·5
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-6\sqrt{31}}{2*50}=\frac{-46-6\sqrt{31}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+6\sqrt{31}}{2*50}=\frac{-46+6\sqrt{31}}{100}
$