6a-7/2a+14=0

Solution for 6a-7/2a+14=0 equation:

6a-7/2a+14=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


6a*2a+14*2a-7=0

Wy multiply elements

12a^2+28a-7=0

a = 12; b = 28; c = -7;
Δ = b2-4ac
Δ = 282-4·12·(-7)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{70}}{2*12}=\frac{-28-4\sqrt{70}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{70}}{2*12}=\frac{-28+4\sqrt{70}}{24}
$