10a^2-11a=-3

Solution for 10a^2-11a=-3 equation:

10a^2-11a=-3

We move all terms to the left:

10a^2-11a-(-3)=0

We add all the numbers together, and all the variables

10a^2-11a+3=0

a = 10; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·10·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*10}=\frac{10}{20}
=1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*10}=\frac{12}{20}
=3/5
$