10a^2-11a=18

Solution for 10a^2-11a=18 equation:

10a^2-11a=18

We move all terms to the left:

10a^2-11a-(18)=0

a = 10; b = -11; c = -18;
Δ = b2-4ac
Δ = -112-4·10·(-18)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*10}=\frac{-18}{20}
=-9/10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*10}=\frac{40}{20}
=2
$