-7x^2+5x+11=0

Solution for -7x^2+5x+11=0 equation:

-7x^2+5x+11=0

a = -7; b = 5; c = +11;
Δ = b2-4ac
Δ = 52-4·(-7)·11
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{37}}{2*-7}=\frac{-5-3\sqrt{37}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{37}}{2*-7}=\frac{-5+3\sqrt{37}}{-14}
$