1/2*4a+10=2a+

Solution for 1/2*4a+10=2a+ equation:

1/2*4a+10=2a+

We move all terms to the left:

1/2*4a+10-(2a+)=0


Domain of the equation: 2*4a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/2*4a-(+2a)+10=0

We get rid of parentheses

1/2*4a-2a+10=0

We multiply all the terms by the denominator


-2a*2*4a+10*2*4a+1=0

Wy multiply elements

-16a^2*4+80a*4+1=0

Wy multiply elements

-64a^2+320a+1=0

a = -64; b = 320; c = +1;
Δ = b2-4ac
Δ = 3202-4·(-64)·1
Δ = 102656
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:

$\sqrt{\Delta}=\sqrt{102656}=\sqrt{256*401}=\sqrt{256}*\sqrt{401}=16\sqrt{401}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-16\sqrt{401}}{2*-64}=\frac{-320-16\sqrt{401}}{-128}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+16\sqrt{401}}{2*-64}=\frac{-320+16\sqrt{401}}{-128}
$