113,43=45,522*x-2,529*x^2

Solution for 113,43=45,522*x-2,529*x^2 equation:

113.43=45.522x-2.529x^2

We move all terms to the left:

113.43-(45.522x-2.529x^2)=0

We get rid of parentheses

2.529x^2-45.522x+113.43=0

a = 2.529; b = -45.522; c = +113.43;
Δ = b2-4ac
Δ = -45.5222-4·2.529·113.43
Δ = 924.794604
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{-(-45.522)-\sqrt{924.794604}}{2*2.529}=\frac{45.522-\sqrt{924.794604}}{5.058}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45.522)+\sqrt{924.794604}}{2*2.529}=\frac{45.522+\sqrt{924.794604}}{5.058}
$