7x(3x+4)=5-8x

Solution for 7x(3x+4)=5-8x equation:

7x(3x+4)=5-8x

We move all terms to the left:

7x(3x+4)-(5-8x)=0

We add all the numbers together, and all the variables

7x(3x+4)-(-8x+5)=0

We multiply parentheses

21x^2+28x-(-8x+5)=0

We get rid of parentheses

21x^2+28x+8x-5=0

We add all the numbers together, and all the variables

21x^2+36x-5=0

a = 21; b = 36; c = -5;
Δ = b2-4ac
Δ = 362-4·21·(-5)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{429}}{2*21}=\frac{-36-2\sqrt{429}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{429}}{2*21}=\frac{-36+2\sqrt{429}}{42}
$