5u^2+12u+4=2

Solution for 5u^2+12u+4=2 equation:

5u^2+12u+4=2

We move all terms to the left:

5u^2+12u+4-(2)=0

We add all the numbers together, and all the variables

5u^2+12u+2=0

a = 5; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·5·2
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*5}=\frac{-12-2\sqrt{26}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*5}=\frac{-12+2\sqrt{26}}{10}
$