4x^2-17x=13=-5x+8

Solution for 4x^2-17x=13=-5x+8 equation:

4x^2-17x=13=-5x+8

We move all terms to the left:

4x^2-17x-(13)=0

a = 4; b = -17; c = -13;
Δ = b2-4ac
Δ = -172-4·4·(-13)
Δ = 497
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{-(-17)-\sqrt{497}}{2*4}=\frac{17-\sqrt{497}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{497}}{2*4}=\frac{17+\sqrt{497}}{8}
$