7r^2-10=102

Solution for 7r^2-10=102 equation:

7r^2-10=102

We move all terms to the left:

7r^2-10-(102)=0

We add all the numbers together, and all the variables

7r^2-112=0

a = 7; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·7·(-112)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56}{2*7}=\frac{-56}{14}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56}{2*7}=\frac{56}{14}
=4
$