2r^2-7r-18=-3

Solution for 2r^2-7r-18=-3 equation:

2r^2-7r-18=-3

We move all terms to the left:

2r^2-7r-18-(-3)=0

We add all the numbers together, and all the variables

2r^2-7r-15=0

a = 2; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·2·(-15)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*2}=\frac{-6}{4}
=-1+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*2}=\frac{20}{4}
=5
$