2r^2-7r=12

Solution for 2r^2-7r=12 equation:

2r^2-7r=12

We move all terms to the left:

2r^2-7r-(12)=0

a = 2; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·2·(-12)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{145}}{2*2}=\frac{7-\sqrt{145}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*2}=\frac{7+\sqrt{145}}{4}
$