175=10x+5x^2

Solution for 175=10x+5x^2 equation:

175=10x+5x^2

We move all terms to the left:

175-(10x+5x^2)=0

We get rid of parentheses

-5x^2-10x+175=0

a = -5; b = -10; c = +175;
Δ = b2-4ac
Δ = -102-4·(-5)·175
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-60}{2*-5}=\frac{-50}{-10}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+60}{2*-5}=\frac{70}{-10}
=-7
$