-7=-11/2b+2b

Solution for -7=-11/2b+2b equation:

-7=-11/2b+2b

We move all terms to the left:

-7-(-11/2b+2b)=0


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

b∈R


We add all the numbers together, and all the variables

-(+2b-11/2b)-7=0

We get rid of parentheses

-2b+11/2b-7=0

We multiply all the terms by the denominator


-2b*2b-7*2b+11=0

Wy multiply elements

-4b^2-14b+11=0

a = -4; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·(-4)·11
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{93}}{2*-4}=\frac{14-2\sqrt{93}}{-8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{93}}{2*-4}=\frac{14+2\sqrt{93}}{-8}
$