46x^2-150x+100=0

Solution for 46x^2-150x+100=0 equation:

46x^2-150x+100=0

a = 46; b = -150; c = +100;
Δ = b2-4ac
Δ = -1502-4·46·100
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{41}}{2*46}=\frac{150-10\sqrt{41}}{92}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{41}}{2*46}=\frac{150+10\sqrt{41}}{92}
$