5x(x+12)+2(-x+5)=-15

Solution for 5x(x+12)+2(-x+5)=-15 equation:

5x(x+12)+2(-x+5)=-15

We move all terms to the left:

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

We add all the numbers together, and all the variables

5x(x+12)+2(-1x+5)-(-15)=0

We add all the numbers together, and all the variables

5x(x+12)+2(-1x+5)+15=0

We multiply parentheses

5x^2+60x-2x+10+15=0

We add all the numbers together, and all the variables

5x^2+58x+25=0

a = 5; b = 58; c = +25;
Δ = b2-4ac
Δ = 582-4·5·25
Δ = 2864
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:

$\sqrt{\Delta}=\sqrt{2864}=\sqrt{16*179}=\sqrt{16}*\sqrt{179}=4\sqrt{179}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-4\sqrt{179}}{2*5}=\frac{-58-4\sqrt{179}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+4\sqrt{179}}{2*5}=\frac{-58+4\sqrt{179}}{10}
$