6x^2+3+8x^2-5+10x-10=180

Solution for 6x^2+3+8x^2-5+10x-10=180 equation:

6x^2+3+8x^2-5+10x-10=180

We move all terms to the left:

6x^2+3+8x^2-5+10x-10-(180)=0

We add all the numbers together, and all the variables

14x^2+10x-192=0

a = 14; b = 10; c = -192;
Δ = b2-4ac
Δ = 102-4·14·(-192)
Δ = 10852
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:

$\sqrt{\Delta}=\sqrt{10852}=\sqrt{4*2713}=\sqrt{4}*\sqrt{2713}=2\sqrt{2713}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2713}}{2*14}=\frac{-10-2\sqrt{2713}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2713}}{2*14}=\frac{-10+2\sqrt{2713}}{28}
$