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

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

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

We move all terms to the left:

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


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 5b+14)!=0

b∈R


We add all the numbers together, and all the variables

3/5b+7b-(-2/5b+26)-2=0

We add all the numbers together, and all the variables

7b+3/5b-(-2/5b+26)-2=0

We get rid of parentheses

7b+3/5b+2/5b-26-2=0

We multiply all the terms by the denominator


7b*5b-26*5b-2*5b+3+2=0

We add all the numbers together, and all the variables

7b*5b-26*5b-2*5b+5=0

Wy multiply elements

35b^2-130b-10b+5=0

We add all the numbers together, and all the variables

35b^2-140b+5=0

a = 35; b = -140; c = +5;
Δ = b2-4ac
Δ = -1402-4·35·5
Δ = 18900
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:

$\sqrt{\Delta}=\sqrt{18900}=\sqrt{900*21}=\sqrt{900}*\sqrt{21}=30\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-30\sqrt{21}}{2*35}=\frac{140-30\sqrt{21}}{70}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+30\sqrt{21}}{2*35}=\frac{140+30\sqrt{21}}{70}
$