4x2-10x+10=100

Solution for 4x2-10x+10=100 equation:

4x^2-10x+10=100

We move all terms to the left:

4x^2-10x+10-(100)=0

We add all the numbers together, and all the variables

4x^2-10x-90=0

a = 4; b = -10; c = -90;
Δ = b2-4ac
Δ = -102-4·4·(-90)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{385}}{2*4}=\frac{10-2\sqrt{385}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{385}}{2*4}=\frac{10+2\sqrt{385}}{8}
$