14r^2+51r=54

Solution for 14r^2+51r=54 equation:

14r^2+51r=54

We move all terms to the left:

14r^2+51r-(54)=0

a = 14; b = 51; c = -54;
Δ = b2-4ac
Δ = 512-4·14·(-54)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*14}=\frac{-126}{28}
=-4+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*14}=\frac{24}{28}
=6/7
$