148-69x+2x^2=0

Solution for 148-69x+2x^2=0 equation:

148-69x+2x^2=0

a = 2; b = -69; c = +148;
Δ = b2-4ac
Δ = -692-4·2·148
Δ = 3577
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:

$\sqrt{\Delta}=\sqrt{3577}=\sqrt{49*73}=\sqrt{49}*\sqrt{73}=7\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-7\sqrt{73}}{2*2}=\frac{69-7\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+7\sqrt{73}}{2*2}=\frac{69+7\sqrt{73}}{4}
$