20x2-30x=2x+45

Solution for 20x2-30x=2x+45 equation:

20x^2-30x=2x+45

We move all terms to the left:

20x^2-30x-(2x+45)=0

We get rid of parentheses

20x^2-30x-2x-45=0

We add all the numbers together, and all the variables

20x^2-32x-45=0

a = 20; b = -32; c = -45;
Δ = b2-4ac
Δ = -322-4·20·(-45)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-68}{2*20}=\frac{-36}{40}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+68}{2*20}=\frac{100}{40}
=2+1/2
$