3q^2=10q+4

Solution for 3q^2=10q+4 equation:

3q^2=10q+4

We move all terms to the left:

3q^2-(10q+4)=0

We get rid of parentheses

3q^2-10q-4=0

a = 3; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·3·(-4)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*3}=\frac{10-2\sqrt{37}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*3}=\frac{10+2\sqrt{37}}{6}
$