10x^2+31x+13=0

Solution for 10x^2+31x+13=0 equation:

10x^2+31x+13=0

a = 10; b = 31; c = +13;
Δ = b2-4ac
Δ = 312-4·10·13
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-21}{2*10}=\frac{-52}{20}
=-2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+21}{2*10}=\frac{-10}{20}
=-1/2
$