5x^2-11x+3=24

Solution for 5x^2-11x+3=24 equation:

5x^2-11x+3=24

We move all terms to the left:

5x^2-11x+3-(24)=0

We add all the numbers together, and all the variables

5x^2-11x-21=0

a = 5; b = -11; c = -21;
Δ = b2-4ac
Δ = -112-4·5·(-21)
Δ = 541
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{541}}{2*5}=\frac{11-\sqrt{541}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{541}}{2*5}=\frac{11+\sqrt{541}}{10}
$