8x^2+13x-19=4x-11

Solution for 8x^2+13x-19=4x-11 equation:

8x^2+13x-19=4x-11

We move all terms to the left:

8x^2+13x-19-(4x-11)=0

We get rid of parentheses

8x^2+13x-4x+11-19=0

We add all the numbers together, and all the variables

8x^2+9x-8=0

a = 8; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·8·(-8)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{337}}{2*8}=\frac{-9-\sqrt{337}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{337}}{2*8}=\frac{-9+\sqrt{337}}{16}
$