7x^2+58x+13=0

Solution for 7x^2+58x+13=0 equation:

7x^2+58x+13=0

a = 7; b = 58; c = +13;
Δ = b2-4ac
Δ = 582-4·7·13
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-10\sqrt{30}}{2*7}=\frac{-58-10\sqrt{30}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+10\sqrt{30}}{2*7}=\frac{-58+10\sqrt{30}}{14}
$