4x^2+45x-83=5x-17

Solution for 4x^2+45x-83=5x-17 equation:

4x^2+45x-83=5x-17

We move all terms to the left:

4x^2+45x-83-(5x-17)=0

We get rid of parentheses

4x^2+45x-5x+17-83=0

We add all the numbers together, and all the variables

4x^2+40x-66=0

a = 4; b = 40; c = -66;
Δ = b2-4ac
Δ = 402-4·4·(-66)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{166}}{2*4}=\frac{-40-4\sqrt{166}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{166}}{2*4}=\frac{-40+4\sqrt{166}}{8}
$