10+65x2=140

Solution for 10+65x2=140 equation:

10+65x^2=140

We move all terms to the left:

10+65x^2-(140)=0

We add all the numbers together, and all the variables

65x^2-130=0

a = 65; b = 0; c = -130;
Δ = b2-4ac
Δ = 02-4·65·(-130)
Δ = 33800
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:

$\sqrt{\Delta}=\sqrt{33800}=\sqrt{16900*2}=\sqrt{16900}*\sqrt{2}=130\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-130\sqrt{2}}{2*65}=\frac{0-130\sqrt{2}}{130}
=-\frac{130\sqrt{2}}{130}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+130\sqrt{2}}{2*65}=\frac{0+130\sqrt{2}}{130}
=\frac{130\sqrt{2}}{130}
=\sqrt{2}
$