5f^2=4(8f-3)

Solution for 5f^2=4(8f-3) equation:

5f^2=4(8f-3)

We move all terms to the left:

5f^2-(4(8f-3))=0


We calculate terms in parentheses: -(4(8f-3)), so:

4(8f-3)

We multiply parentheses

32f-12

Back to the equation:

-(32f-12)


We get rid of parentheses

5f^2-32f+12=0

a = 5; b = -32; c = +12;
Δ = b2-4ac
Δ = -322-4·5·12
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-28}{2*5}=\frac{4}{10}
=2/5
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+28}{2*5}=\frac{60}{10}
=6
$