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

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

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

We move all terms to the left:

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


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 5b+4)!=0

b∈R


We add all the numbers together, and all the variables

3/5b+7b-(-2/5b+16)-2=0

We add all the numbers together, and all the variables

7b+3/5b-(-2/5b+16)-2=0

We get rid of parentheses

7b+3/5b+2/5b-16-2=0

We multiply all the terms by the denominator


7b*5b-16*5b-2*5b+3+2=0

We add all the numbers together, and all the variables

7b*5b-16*5b-2*5b+5=0

Wy multiply elements

35b^2-80b-10b+5=0

We add all the numbers together, and all the variables

35b^2-90b+5=0

a = 35; b = -90; c = +5;
Δ = b2-4ac
Δ = -902-4·35·5
Δ = 7400
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:

$\sqrt{\Delta}=\sqrt{7400}=\sqrt{100*74}=\sqrt{100}*\sqrt{74}=10\sqrt{74}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{74}}{2*35}=\frac{90-10\sqrt{74}}{70}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{74}}{2*35}=\frac{90+10\sqrt{74}}{70}
$