2x^2-38x+361=193

Solution for 2x^2-38x+361=193 equation:

2x^2-38x+361=193

We move all terms to the left:

2x^2-38x+361-(193)=0

We add all the numbers together, and all the variables

2x^2-38x+168=0

a = 2; b = -38; c = +168;
Δ = b2-4ac
Δ = -382-4·2·168
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{-(-38)-10}{2*2}=\frac{28}{4}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+10}{2*2}=\frac{48}{4}
=12
$