2x+58x2=180

Solution for 2x+58x2=180 equation:

2x+58x^2=180

We move all terms to the left:

2x+58x^2-(180)=0

a = 58; b = 2; c = -180;
Δ = b2-4ac
Δ = 22-4·58·(-180)
Δ = 41764
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:

$\sqrt{\Delta}=\sqrt{41764}=\sqrt{4*10441}=\sqrt{4}*\sqrt{10441}=2\sqrt{10441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{10441}}{2*58}=\frac{-2-2\sqrt{10441}}{116}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{10441}}{2*58}=\frac{-2+2\sqrt{10441}}{116}
$