4x^2-15=17x

Solution for 4x^2-15=17x equation:

4x^2-15=17x

We move all terms to the left:

4x^2-15-(17x)=0

a = 4; b = -17; c = -15;
Δ = b2-4ac
Δ = -172-4·4·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*4}=\frac{40}{8}
=5
$