42r^2-30r=0

Solution for 42r^2-30r=0 equation:

42r^2-30r=0

a = 42; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·42·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*42}=\frac{0}{84}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*42}=\frac{60}{84}
=5/7
$