-3(14+5r)2r=-14(r+3)

Solution for -3(14+5r)2r=-14(r+3) equation:

-3(14+5r)2r=-14(r+3)

We move all terms to the left:

-3(14+5r)2r-(-14(r+3))=0

We add all the numbers together, and all the variables

-3(5r+14)2r-(-14(r+3))=0

We multiply parentheses

-30r^2-84r-(-14(r+3))=0


We calculate terms in parentheses: -(-14(r+3)), so:

-14(r+3)

We multiply parentheses

-14r-42

Back to the equation:

-(-14r-42)


We get rid of parentheses

-30r^2-84r+14r+42=0

We add all the numbers together, and all the variables

-30r^2-70r+42=0

a = -30; b = -70; c = +42;
Δ = b2-4ac
Δ = -702-4·(-30)·42
Δ = 9940
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:

$\sqrt{\Delta}=\sqrt{9940}=\sqrt{4*2485}=\sqrt{4}*\sqrt{2485}=2\sqrt{2485}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{2485}}{2*-30}=\frac{70-2\sqrt{2485}}{-60}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{2485}}{2*-30}=\frac{70+2\sqrt{2485}}{-60}
$