3(5x+7)-8x(x-2)=-26

Solution for 3(5x+7)-8x(x-2)=-26 equation:

3(5x+7)-8x(x-2)=-26

We move all terms to the left:

3(5x+7)-8x(x-2)-(-26)=0

We add all the numbers together, and all the variables

3(5x+7)-8x(x-2)+26=0

We multiply parentheses

-8x^2+15x+16x+21+26=0

We add all the numbers together, and all the variables

-8x^2+31x+47=0

a = -8; b = 31; c = +47;
Δ = b2-4ac
Δ = 312-4·(-8)·47
Δ = 2465
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{-(31)-\sqrt{2465}}{2*-8}=\frac{-31-\sqrt{2465}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{2465}}{2*-8}=\frac{-31+\sqrt{2465}}{-16}
$