45x+x2=2079

Solution for 45x+x2=2079 equation:

45x+x2=2079

We move all terms to the left:

45x+x2-(2079)=0

We add all the numbers together, and all the variables

x^2+45x-2079=0

a = 1; b = 45; c = -2079;
Δ = b2-4ac
Δ = 452-4·1·(-2079)
Δ = 10341
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:

$\sqrt{\Delta}=\sqrt{10341}=\sqrt{9*1149}=\sqrt{9}*\sqrt{1149}=3\sqrt{1149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{1149}}{2*1}=\frac{-45-3\sqrt{1149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{1149}}{2*1}=\frac{-45+3\sqrt{1149}}{2}
$