(3a+14/2a-2)-2a=7

Solution for (3a+14/2a-2)-2a=7 equation:

(3a+14/2a-2)-2a=7

We move all terms to the left:

(3a+14/2a-2)-2a-(7)=0


Domain of the equation: 2a-2)!=0

a∈R


We add all the numbers together, and all the variables

-2a+(3a+14/2a-2)-7=0

We get rid of parentheses

-2a+3a+14/2a-2-7=0

We multiply all the terms by the denominator


-2a*2a+3a*2a-2*2a-7*2a+14=0

Wy multiply elements

-4a^2+6a^2-4a-14a+14=0

We add all the numbers together, and all the variables

2a^2-18a+14=0

a = 2; b = -18; c = +14;
Δ = b2-4ac
Δ = -182-4·2·14
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{53}}{2*2}=\frac{18-2\sqrt{53}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{53}}{2*2}=\frac{18+2\sqrt{53}}{4}
$