-5x^2+18x=11

Solution for -5x^2+18x=11 equation:

-5x^2+18x=11

We move all terms to the left:

-5x^2+18x-(11)=0

a = -5; b = 18; c = -11;
Δ = b2-4ac
Δ = 182-4·(-5)·(-11)
Δ = 104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{26}}{2*-5}=\frac{-18-2\sqrt{26}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{26}}{2*-5}=\frac{-18+2\sqrt{26}}{-10}
$