14x^2+31x=10

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

14x^2+31x=10

We move all terms to the left:

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
$