7/2a+7=35a=8

Solution for 7/2a+7=35a=8 equation:

7/2a+7=35a=8

We move all terms to the left:

7/2a+7-(35a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-35a+7/2a+7=0

We multiply all the terms by the denominator


-35a*2a+7*2a+7=0

Wy multiply elements

-70a^2+14a+7=0

a = -70; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-70)·7
Δ = 2156
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:

$\sqrt{\Delta}=\sqrt{2156}=\sqrt{196*11}=\sqrt{196}*\sqrt{11}=14\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{11}}{2*-70}=\frac{-14-14\sqrt{11}}{-140}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{11}}{2*-70}=\frac{-14+14\sqrt{11}}{-140}
$