-5*x*(3*x+4)=-29+8*x

Solution for -5*x*(3*x+4)=-29+8*x equation:

-5x(3x+4)=-29+8x

We move all terms to the left:

-5x(3x+4)-(-29+8x)=0

We add all the numbers together, and all the variables

-5x(3x+4)-(8x-29)=0

We multiply parentheses

-15x^2-20x-(8x-29)=0

We get rid of parentheses

-15x^2-20x-8x+29=0

We add all the numbers together, and all the variables

-15x^2-28x+29=0

a = -15; b = -28; c = +29;
Δ = b2-4ac
Δ = -282-4·(-15)·29
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{631}}{2*-15}=\frac{28-2\sqrt{631}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{631}}{2*-15}=\frac{28+2\sqrt{631}}{-30}
$