x2+14x-15=8x-9

Solution for x2+14x-15=8x-9 equation:

x2+14x-15=8x-9

We move all terms to the left:

x2+14x-15-(8x-9)=0

We add all the numbers together, and all the variables

x^2+14x-(8x-9)-15=0

We get rid of parentheses

x^2+14x-8x+9-15=0

We add all the numbers together, and all the variables

x^2+6x-6=0

a = 1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·1·(-6)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*1}=\frac{-6-2\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*1}=\frac{-6+2\sqrt{15}}{2}
$