0=4x^2-6x-7

Solution for 0=4x^2-6x-7 equation:

0=4x^2-6x-7

We move all terms to the left:

0-(4x^2-6x-7)=0

We add all the numbers together, and all the variables

-(4x^2-6x-7)=0

We get rid of parentheses

-4x^2+6x+7=0

a = -4; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-4)·7
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*-4}=\frac{-6-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*-4}=\frac{-6+2\sqrt{37}}{-8}
$