x^2=15x-34

Solution for x^2=15x-34 equation:

x^2=15x-34

We move all terms to the left:

x^2-(15x-34)=0

We get rid of parentheses

x^2-15x+34=0

a = 1; b = -15; c = +34;
Δ = b2-4ac
Δ = -152-4·1·34
Δ = 89
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{-(-15)-\sqrt{89}}{2*1}=\frac{15-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{89}}{2*1}=\frac{15+\sqrt{89}}{2}
$