112.5=(x+3.5)x

Solution for 112.5=(x+3.5)x equation:

112.5=(x+3.5)x

We move all terms to the left:

112.5-((x+3.5)x)=0


We calculate terms in parentheses: -((x+3.5)x), so:

(x+3.5)x

We multiply parentheses

x^2+3.5x

Back to the equation:

-(x^2+3.5x)


We get rid of parentheses

-x^2-3.5x+112.5=0

We add all the numbers together, and all the variables

-1x^2-3.5x+112.5=0

a = -1; b = -3.5; c = +112.5;
Δ = b2-4ac
Δ = -3.52-4·(-1)·112.5
Δ = 462.25
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{462.25}}{2*-1}=\frac{3.5-\sqrt{462.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.5)+\sqrt{462.25}}{2*-1}=\frac{3.5+\sqrt{462.25}}{-2}
$