2x^2+4900-1400x-2500=120

Solution for 2x^2+4900-1400x-2500=120 equation:

2x^2+4900-1400x-2500=120

We move all terms to the left:

2x^2+4900-1400x-2500-(120)=0

We add all the numbers together, and all the variables

2x^2-1400x+2280=0

a = 2; b = -1400; c = +2280;
Δ = b2-4ac
Δ = -14002-4·2·2280
Δ = 1941760
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:

$\sqrt{\Delta}=\sqrt{1941760}=\sqrt{256*7585}=\sqrt{256}*\sqrt{7585}=16\sqrt{7585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-16\sqrt{7585}}{2*2}=\frac{1400-16\sqrt{7585}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+16\sqrt{7585}}{2*2}=\frac{1400+16\sqrt{7585}}{4}
$