35x^2=31x+40

Solution for 35x^2=31x+40 equation:

35x^2=31x+40

We move all terms to the left:

35x^2-(31x+40)=0

We get rid of parentheses

35x^2-31x-40=0

a = 35; b = -31; c = -40;
Δ = b2-4ac
Δ = -312-4·35·(-40)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-81}{2*35}=\frac{-50}{70}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+81}{2*35}=\frac{112}{70}
=1+3/5
$