5.2a(2a-1)=7a+14.6

Solution for 5.2a(2a-1)=7a+14.6 equation:

5.2a(2a-1)=7a+14.6

We move all terms to the left:

5.2a(2a-1)-(7a+14.6)=0

We multiply parentheses

10a^2-5a-(7a+14.6)=0

We get rid of parentheses

10a^2-5a-7a-14.6=0

We add all the numbers together, and all the variables

10a^2-12a-14.6=0

a = 10; b = -12; c = -14.6;
Δ = b2-4ac
Δ = -122-4·10·(-14.6)
Δ = 728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{182}}{2*10}=\frac{12-2\sqrt{182}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{182}}{2*10}=\frac{12+2\sqrt{182}}{20}
$