-14x^2+31x+10=0

Solution for -14x^2+31x+10=0 equation:

-14x^2+31x+10=0

a = -14; b = 31; c = +10;
Δ = b2-4ac
Δ = 312-4·(-14)·10
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-39}{2*-14}=\frac{-70}{-28}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+39}{2*-14}=\frac{8}{-28}
=-2/7
$