5q^2-7q+4=6

Solution for 5q^2-7q+4=6 equation:

5q^2-7q+4=6

We move all terms to the left:

5q^2-7q+4-(6)=0

We add all the numbers together, and all the variables

5q^2-7q-2=0

a = 5; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·5·(-2)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{89}}{2*5}=\frac{7-\sqrt{89}}{10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*5}=\frac{7+\sqrt{89}}{10}
$