5x^2-12x=-6x+15

Solution for 5x^2-12x=-6x+15 equation:

5x^2-12x=-6x+15

We move all terms to the left:

5x^2-12x-(-6x+15)=0

We get rid of parentheses

5x^2-12x+6x-15=0

We add all the numbers together, and all the variables

5x^2-6x-15=0

a = 5; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·5·(-15)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{21}}{2*5}=\frac{6-4\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{21}}{2*5}=\frac{6+4\sqrt{21}}{10}
$