2-4x2=10x+5

Solution for 2-4x2=10x+5 equation:

2-4x^2=10x+5

We move all terms to the left:

2-4x^2-(10x+5)=0

We get rid of parentheses

-4x^2-10x-5+2=0

We add all the numbers together, and all the variables

-4x^2-10x-3=0

a = -4; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·(-4)·(-3)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*-4}=\frac{10-2\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*-4}=\frac{10+2\sqrt{13}}{-8}
$