48x^2-238x+171=3-x^2

Solution for 48x^2-238x+171=3-x^2 equation:

48x^2-238x+171=3-x^2

We move all terms to the left:

48x^2-238x+171-(3-x^2)=0

We get rid of parentheses

48x^2+x^2-238x-3+171=0

We add all the numbers together, and all the variables

49x^2-238x+168=0

a = 49; b = -238; c = +168;
Δ = b2-4ac
Δ = -2382-4·49·168
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-238)-154}{2*49}=\frac{84}{98}
=6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-238)+154}{2*49}=\frac{392}{98}
=4
$