4x^2-10=10-20x

Solution for 4x^2-10=10-20x equation:

4x^2-10=10-20x

We move all terms to the left:

4x^2-10-(10-20x)=0

We add all the numbers together, and all the variables

4x^2-(-20x+10)-10=0

We get rid of parentheses

4x^2+20x-10-10=0

We add all the numbers together, and all the variables

4x^2+20x-20=0

a = 4; b = 20; c = -20;
Δ = b2-4ac
Δ = 202-4·4·(-20)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{5}}{2*4}=\frac{-20-12\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{5}}{2*4}=\frac{-20+12\sqrt{5}}{8}
$