2k^2-15k=5-2

Solution for 2k^2-15k=5-2 equation:

2k^2-15k=5-2

We move all terms to the left:

2k^2-15k-(5-2)=0

We add all the numbers together, and all the variables

2k^2-15k-3=0

a = 2; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·2·(-3)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{249}}{2*2}=\frac{15-\sqrt{249}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*2}=\frac{15+\sqrt{249}}{4}
$