10r=6-4r2

Solution for 10r=6-4r2 equation:

10r=6-4r^2

We move all terms to the left:

10r-(6-4r^2)=0

We get rid of parentheses

4r^2+10r-6=0

a = 4; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·4·(-6)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*4}=\frac{-24}{8}
=-3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*4}=\frac{4}{8}
=1/2
$