2/5b+-3=2b+-18

Solution for 2/5b+-3=2b+-18 equation:

2/5b+-3=2b+-18

We move all terms to the left:

2/5b+-3-(2b+-18)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

2/5b-(2b-18)-3+=0

We add all the numbers together, and all the variables

2/5b-(2b-18)=0

We get rid of parentheses

2/5b-2b+18=0

We multiply all the terms by the denominator


-2b*5b+18*5b+2=0

Wy multiply elements

-10b^2+90b+2=0

a = -10; b = 90; c = +2;
Δ = b2-4ac
Δ = 902-4·(-10)·2
Δ = 8180
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:

$\sqrt{\Delta}=\sqrt{8180}=\sqrt{4*2045}=\sqrt{4}*\sqrt{2045}=2\sqrt{2045}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2045}}{2*-10}=\frac{-90-2\sqrt{2045}}{-20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2045}}{2*-10}=\frac{-90+2\sqrt{2045}}{-20}
$