8x^2+38x+35=13

Solution for 8x^2+38x+35=13 equation:

8x^2+38x+35=13

We move all terms to the left:

8x^2+38x+35-(13)=0

We add all the numbers together, and all the variables

8x^2+38x+22=0

a = 8; b = 38; c = +22;
Δ = b2-4ac
Δ = 382-4·8·22
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{185}}{2*8}=\frac{-38-2\sqrt{185}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{185}}{2*8}=\frac{-38+2\sqrt{185}}{16}
$