310=2q+15+250/q

Solution for 310=2q+15+250/q equation:

310=2q+15+250/q

We move all terms to the left:

310-(2q+15+250/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

-(2q+250/q+15)+310=0

We get rid of parentheses

-2q-250/q-15+310=0

We multiply all the terms by the denominator


-2q*q-15*q+310*q-250=0

We add all the numbers together, and all the variables

295q-2q*q-250=0

Wy multiply elements

-2q^2+295q-250=0

a = -2; b = 295; c = -250;
Δ = b2-4ac
Δ = 2952-4·(-2)·(-250)
Δ = 85025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{85025}=\sqrt{25*3401}=\sqrt{25}*\sqrt{3401}=5\sqrt{3401}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(295)-5\sqrt{3401}}{2*-2}=\frac{-295-5\sqrt{3401}}{-4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(295)+5\sqrt{3401}}{2*-2}=\frac{-295+5\sqrt{3401}}{-4}
$