5u2+8u=3

Solution for 5u2+8u=3 equation:

5u^2+8u=3

We move all terms to the left:

5u^2+8u-(3)=0

a = 5; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·5·(-3)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*5}=\frac{-8-2\sqrt{31}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*5}=\frac{-8+2\sqrt{31}}{10}
$