r.45=7+1/2r

Solution for r.45=7+1/2r equation:

r.45=7+1/2r

We move all terms to the left:

r.45-(7+1/2r)=0


Domain of the equation: 2r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

r.45-(1/2r+7)=0

We get rid of parentheses

r.45-1/2r-7=0

We multiply all the terms by the denominator


(r.45)*2r-7*2r-1=0

We add all the numbers together, and all the variables

(+r.45)*2r-7*2r-1=0

We multiply parentheses

2r^2-7*2r-1=0

Wy multiply elements

2r^2-14r-1=0

a = 2; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·2·(-1)
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*2}=\frac{14-2\sqrt{51}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*2}=\frac{14+2\sqrt{51}}{4}
$