45x^2+30x+5=30

Solution for 45x^2+30x+5=30 equation:

45x^2+30x+5=30

We move all terms to the left:

45x^2+30x+5-(30)=0

We add all the numbers together, and all the variables

45x^2+30x-25=0

a = 45; b = 30; c = -25;
Δ = b2-4ac
Δ = 302-4·45·(-25)
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{6}}{2*45}=\frac{-30-30\sqrt{6}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{6}}{2*45}=\frac{-30+30\sqrt{6}}{90}
$