-5(3b-4)=1/2b+2b-120

Solution for -5(3b-4)=1/2b+2b-120 equation:

-5(3b-4)=1/2b+2b-120

We move all terms to the left:

-5(3b-4)-(1/2b+2b-120)=0


Domain of the equation: 2b+2b-120)!=0

b∈R


We add all the numbers together, and all the variables

-5(3b-4)-(2b+1/2b-120)=0

We multiply parentheses

-15b-(2b+1/2b-120)+20=0

We get rid of parentheses

-15b-2b-1/2b+120+20=0

We multiply all the terms by the denominator


-15b*2b-2b*2b+120*2b+20*2b-1=0

Wy multiply elements

-30b^2-4b^2+240b+40b-1=0

We add all the numbers together, and all the variables

-34b^2+280b-1=0

a = -34; b = 280; c = -1;
Δ = b2-4ac
Δ = 2802-4·(-34)·(-1)
Δ = 78264
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:

$\sqrt{\Delta}=\sqrt{78264}=\sqrt{36*2174}=\sqrt{36}*\sqrt{2174}=6\sqrt{2174}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-6\sqrt{2174}}{2*-34}=\frac{-280-6\sqrt{2174}}{-68}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+6\sqrt{2174}}{2*-34}=\frac{-280+6\sqrt{2174}}{-68}
$