5x^2-11x=3

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

5x^2-11x=3

We move all terms to the left:

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

a = 5; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·5·(-3)
Δ = 181
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{181}}{2*5}=\frac{11-\sqrt{181}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*5}=\frac{11+\sqrt{181}}{10}
$