5x^2+4x-1=7

Solution for 5x^2+4x-1=7 equation:

5x^2+4x-1=7

We move all terms to the left:

5x^2+4x-1-(7)=0

We add all the numbers together, and all the variables

5x^2+4x-8=0

a = 5; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·5·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*5}=\frac{-4-4\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*5}=\frac{-4+4\sqrt{11}}{10}
$