7a^2=18a-11

Solution for 7a^2=18a-11 equation:

7a^2=18a-11

We move all terms to the left:

7a^2-(18a-11)=0

We get rid of parentheses

7a^2-18a+11=0

a = 7; b = -18; c = +11;
Δ = b2-4ac
Δ = -182-4·7·11
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4}{2*7}=\frac{14}{14}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4}{2*7}=\frac{22}{14}
=1+4/7
$