31x(x-7)=15

Solution for 31x(x-7)=15 equation:

31x(x-7)=15

We move all terms to the left:

31x(x-7)-(15)=0

We multiply parentheses

31x^2-217x-15=0

a = 31; b = -217; c = -15;
Δ = b2-4ac
Δ = -2172-4·31·(-15)
Δ = 48949
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-217)-\sqrt{48949}}{2*31}=\frac{217-\sqrt{48949}}{62}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-217)+\sqrt{48949}}{2*31}=\frac{217+\sqrt{48949}}{62}
$