1/2a-7=-15+2a

Solution for 1/2a-7=-15+2a equation:

1/2a-7=-15+2a

We move all terms to the left:

1/2a-7-(-15+2a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

1/2a-(2a-15)-7=0

We get rid of parentheses

1/2a-2a+15-7=0

We multiply all the terms by the denominator


-2a*2a+15*2a-7*2a+1=0

Wy multiply elements

-4a^2+30a-14a+1=0

We add all the numbers together, and all the variables

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

a = -4; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-4)·1
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{17}}{2*-4}=\frac{-16-4\sqrt{17}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{17}}{2*-4}=\frac{-16+4\sqrt{17}}{-8}
$