10x^2+19-10x=180

Solution for 10x^2+19-10x=180 equation:

10x^2+19-10x=180

We move all terms to the left:

10x^2+19-10x-(180)=0

We add all the numbers together, and all the variables

10x^2-10x-161=0

a = 10; b = -10; c = -161;
Δ = b2-4ac
Δ = -102-4·10·(-161)
Δ = 6540
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:

$\sqrt{\Delta}=\sqrt{6540}=\sqrt{4*1635}=\sqrt{4}*\sqrt{1635}=2\sqrt{1635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1635}}{2*10}=\frac{10-2\sqrt{1635}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1635}}{2*10}=\frac{10+2\sqrt{1635}}{20}
$