5x^2+18x+4=12x+39

Solution for 5x^2+18x+4=12x+39 equation:

5x^2+18x+4=12x+39

We move all terms to the left:

5x^2+18x+4-(12x+39)=0

We get rid of parentheses

5x^2+18x-12x-39+4=0

We add all the numbers together, and all the variables

5x^2+6x-35=0

a = 5; b = 6; c = -35;
Δ = b2-4ac
Δ = 62-4·5·(-35)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{46}}{2*5}=\frac{-6-4\sqrt{46}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{46}}{2*5}=\frac{-6+4\sqrt{46}}{10}
$