x*x+15=x+45*x+25*x+40

Solution for x*x+15=x+45*x+25*x+40 equation:

x*x+15=x+45*x+25*x+40

We move all terms to the left:

x*x+15-(x+45*x+25*x+40)=0

We add all the numbers together, and all the variables

x*x-(71x+40)+15=0

Wy multiply elements

x^2-(71x+40)+15=0

We get rid of parentheses

x^2-71x-40+15=0

We add all the numbers together, and all the variables

x^2-71x-25=0

a = 1; b = -71; c = -25;
Δ = b2-4ac
Δ = -712-4·1·(-25)
Δ = 5141
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{-(-71)-\sqrt{5141}}{2*1}=\frac{71-\sqrt{5141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{5141}}{2*1}=\frac{71+\sqrt{5141}}{2}
$