45x^2+59=123

Solution for 45x^2+59=123 equation:

45x^2+59=123

We move all terms to the left:

45x^2+59-(123)=0

We add all the numbers together, and all the variables

45x^2-64=0

a = 45; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·45·(-64)
Δ = 11520
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:

$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{5}}{2*45}=\frac{0-48\sqrt{5}}{90}
=-\frac{48\sqrt{5}}{90}
=-\frac{8\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{5}}{2*45}=\frac{0+48\sqrt{5}}{90}
=\frac{48\sqrt{5}}{90}
=\frac{8\sqrt{5}}{15}
$