(x^2/12)+(43-2x)=90

Solution for (x^2/12)+(43-2x)=90 equation:

(x^2/12)+(43-2x)=90

We move all terms to the left:

(x^2/12)+(43-2x)-(90)=0

We add all the numbers together, and all the variables

(x^2/12)+(-2x+43)-90=0

We get rid of parentheses

x^2/12-2x+43-90=0

We multiply all the terms by the denominator


x^2-2x*12+43*12-90*12=0

We add all the numbers together, and all the variables

x^2-2x*12-564=0

Wy multiply elements

x^2-24x-564=0

a = 1; b = -24; c = -564;
Δ = b2-4ac
Δ = -242-4·1·(-564)
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{177}}{2*1}=\frac{24-4\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{177}}{2*1}=\frac{24+4\sqrt{177}}{2}
$