3/5b-2+7b-12-2/5b+14=4

Solution for 3/5b-2+7b-12-2/5b+14=4 equation:

3/5b-2+7b-12-2/5b+14=4

We move all terms to the left:

3/5b-2+7b-12-2/5b+14-(4)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

7b+3/5b-2/5b-4=0

We multiply all the terms by the denominator


7b*5b-4*5b+3-2=0

We add all the numbers together, and all the variables

7b*5b-4*5b+1=0

Wy multiply elements

35b^2-20b+1=0

a = 35; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·35·1
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{65}}{2*35}=\frac{20-2\sqrt{65}}{70}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{65}}{2*35}=\frac{20+2\sqrt{65}}{70}
$