0=1x^2-7x-4

Solution for 0=1x^2-7x-4 equation:

0=1x^2-7x-4

We move all terms to the left:

0-(1x^2-7x-4)=0

We add all the numbers together, and all the variables

-(1x^2-7x-4)=0

We get rid of parentheses

-1x^2+7x+4=0

a = -1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-1)·4
Δ = 65
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{-(7)-\sqrt{65}}{2*-1}=\frac{-7-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-1}=\frac{-7+\sqrt{65}}{-2}
$