3f(2)=4(2)-5

Solution for 3f(2)=4(2)-5 equation:

3f(2)=4(2)-5

We move all terms to the left:

3f(2)-(4(2)-5)=0

We add all the numbers together, and all the variables

3f2-37=0

We add all the numbers together, and all the variables

3f^2-37=0

a = 3; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·3·(-37)
Δ = 444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{111}}{2*3}=\frac{0-2\sqrt{111}}{6}
=-\frac{2\sqrt{111}}{6}
=-\frac{\sqrt{111}}{3}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{111}}{2*3}=\frac{0+2\sqrt{111}}{6}
=\frac{2\sqrt{111}}{6}
=\frac{\sqrt{111}}{3}
$