2x(-3x-10)=4x-35

Solution for 2x(-3x-10)=4x-35 equation:

2x(-3x-10)=4x-35

We move all terms to the left:

2x(-3x-10)-(4x-35)=0

We multiply parentheses

-6x^2-20x-(4x-35)=0

We get rid of parentheses

-6x^2-20x-4x+35=0

We add all the numbers together, and all the variables

-6x^2-24x+35=0

a = -6; b = -24; c = +35;
Δ = b2-4ac
Δ = -242-4·(-6)·35
Δ = 1416
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:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{354}}{2*-6}=\frac{24-2\sqrt{354}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{354}}{2*-6}=\frac{24+2\sqrt{354}}{-12}
$