2x2+19x+34=5x+15

Solution for 2x2+19x+34=5x+15 equation:

2x^2+19x+34=5x+15

We move all terms to the left:

2x^2+19x+34-(5x+15)=0

We get rid of parentheses

2x^2+19x-5x-15+34=0

We add all the numbers together, and all the variables

2x^2+14x+19=0

a = 2; b = 14; c = +19;
Δ = b2-4ac
Δ = 142-4·2·19
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{11}}{2*2}=\frac{-14-2\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{11}}{2*2}=\frac{-14+2\sqrt{11}}{4}
$