4x^2-30x+50=100

Solution for 4x^2-30x+50=100 equation:

4x^2-30x+50=100

We move all terms to the left:

4x^2-30x+50-(100)=0

We add all the numbers together, and all the variables

4x^2-30x-50=0

a = 4; b = -30; c = -50;
Δ = b2-4ac
Δ = -302-4·4·(-50)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{17}}{2*4}=\frac{30-10\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{17}}{2*4}=\frac{30+10\sqrt{17}}{8}
$