5x(4-3x)+2=-7

Solution for 5x(4-3x)+2=-7 equation:

5x(4-3x)+2=-7

We move all terms to the left:

5x(4-3x)+2-(-7)=0

We add all the numbers together, and all the variables

5x(-3x+4)+2-(-7)=0

We add all the numbers together, and all the variables

5x(-3x+4)+9=0

We multiply parentheses

-15x^2+20x+9=0

a = -15; b = 20; c = +9;
Δ = b2-4ac
Δ = 202-4·(-15)·9
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{235}}{2*-15}=\frac{-20-2\sqrt{235}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{235}}{2*-15}=\frac{-20+2\sqrt{235}}{-30}
$