4a^2-3a-11=10

Solution for 4a^2-3a-11=10 equation:

4a^2-3a-11=10

We move all terms to the left:

4a^2-3a-11-(10)=0

We add all the numbers together, and all the variables

4a^2-3a-21=0

a = 4; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·4·(-21)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{345}}{2*4}=\frac{3-\sqrt{345}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{345}}{2*4}=\frac{3+\sqrt{345}}{8}
$