x^2+46x+35=0

Solution for x^2+46x+35=0 equation:

x^2+46x+35=0

a = 1; b = 46; c = +35;
Δ = b2-4ac
Δ = 462-4·1·35
Δ = 1976
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:

$\sqrt{\Delta}=\sqrt{1976}=\sqrt{4*494}=\sqrt{4}*\sqrt{494}=2\sqrt{494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{494}}{2*1}=\frac{-46-2\sqrt{494}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{494}}{2*1}=\frac{-46+2\sqrt{494}}{2}
$