120=3.5x+1.75x^2

Solution for 120=3.5x+1.75x^2 equation:

120=3.5x+1.75x^2

We move all terms to the left:

120-(3.5x+1.75x^2)=0

We get rid of parentheses

-1.75x^2-3.5x+120=0

a = -1.75; b = -3.5; c = +120;
Δ = b2-4ac
Δ = -3.52-4·(-1.75)·120
Δ = 852.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3.5)-\sqrt{852.25}}{2*-1.75}=\frac{3.5-\sqrt{852.25}}{-3.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.5)+\sqrt{852.25}}{2*-1.75}=\frac{3.5+\sqrt{852.25}}{-3.5}
$