x2+11x-15=6x-12

Solution for x2+11x-15=6x-12 equation:

x2+11x-15=6x-12

We move all terms to the left:

x2+11x-15-(6x-12)=0

We add all the numbers together, and all the variables

x^2+11x-(6x-12)-15=0

We get rid of parentheses

x^2+11x-6x+12-15=0

We add all the numbers together, and all the variables

x^2+5x-3=0

a = 1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·1·(-3)
Δ = 37
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{-(5)-\sqrt{37}}{2*1}=\frac{-5-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*1}=\frac{-5+\sqrt{37}}{2}
$