-3x(2x+10)=2(-4x+5)

Solution for -3x(2x+10)=2(-4x+5) equation:

-3x(2x+10)=2(-4x+5)

We move all terms to the left:

-3x(2x+10)-(2(-4x+5))=0

We multiply parentheses

-6x^2-30x-(2(-4x+5))=0


We calculate terms in parentheses: -(2(-4x+5)), so:

2(-4x+5)

We multiply parentheses

-8x+10

Back to the equation:

-(-8x+10)


We get rid of parentheses

-6x^2-30x+8x-10=0

We add all the numbers together, and all the variables

-6x^2-22x-10=0

a = -6; b = -22; c = -10;
Δ = b2-4ac
Δ = -222-4·(-6)·(-10)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{61}}{2*-6}=\frac{22-2\sqrt{61}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{61}}{2*-6}=\frac{22+2\sqrt{61}}{-12}
$