7x^2-6x+8x^2-16=180

Solution for 7x^2-6x+8x^2-16=180 equation:

7x^2-6x+8x^2-16=180

We move all terms to the left:

7x^2-6x+8x^2-16-(180)=0

We add all the numbers together, and all the variables

15x^2-6x-196=0

a = 15; b = -6; c = -196;
Δ = b2-4ac
Δ = -62-4·15·(-196)
Δ = 11796
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:

$\sqrt{\Delta}=\sqrt{11796}=\sqrt{4*2949}=\sqrt{4}*\sqrt{2949}=2\sqrt{2949}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{2949}}{2*15}=\frac{6-2\sqrt{2949}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{2949}}{2*15}=\frac{6+2\sqrt{2949}}{30}
$