100=-1.75x^2+30x

Solution for 100=-1.75x^2+30x equation:

100=-1.75x^2+30x

We move all terms to the left:

100-(-1.75x^2+30x)=0

We get rid of parentheses

1.75x^2-30x+100=0

a = 1.75; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·1.75·100
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{2}}{2*1.75}=\frac{30-10\sqrt{2}}{3.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{2}}{2*1.75}=\frac{30+10\sqrt{2}}{3.5}
$