0=7x^2-4x-38

Solution for 0=7x^2-4x-38 equation:

0=7x^2-4x-38

We move all terms to the left:

0-(7x^2-4x-38)=0

We add all the numbers together, and all the variables

-(7x^2-4x-38)=0

We get rid of parentheses

-7x^2+4x+38=0

a = -7; b = 4; c = +38;
Δ = b2-4ac
Δ = 42-4·(-7)·38
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{30}}{2*-7}=\frac{-4-6\sqrt{30}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{30}}{2*-7}=\frac{-4+6\sqrt{30}}{-14}
$