45x2+10=x+20

Solution for 45x2+10=x+20 equation:

45x^2+10=x+20

We move all terms to the left:

45x^2+10-(x+20)=0

We get rid of parentheses

45x^2-x-20+10=0

We add all the numbers together, and all the variables

45x^2-1x-10=0

a = 45; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·45·(-10)
Δ = 1801
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{-(-1)-\sqrt{1801}}{2*45}=\frac{1-\sqrt{1801}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1801}}{2*45}=\frac{1+\sqrt{1801}}{90}
$