6a^2=34a-48

Solution for 6a^2=34a-48 equation:

6a^2=34a-48

We move all terms to the left:

6a^2-(34a-48)=0

We get rid of parentheses

6a^2-34a+48=0

a = 6; b = -34; c = +48;
Δ = b2-4ac
Δ = -342-4·6·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*6}=\frac{32}{12}
=2+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*6}=\frac{36}{12}
=3
$