18-4x-5x^2=3

Solution for 18-4x-5x^2=3 equation:

18-4x-5x^2=3

We move all terms to the left:

18-4x-5x^2-(3)=0

We add all the numbers together, and all the variables

-5x^2-4x+15=0

a = -5; b = -4; c = +15;
Δ = b2-4ac
Δ = -42-4·(-5)·15
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{79}}{2*-5}=\frac{4-2\sqrt{79}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{79}}{2*-5}=\frac{4+2\sqrt{79}}{-10}
$