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

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

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

We move all terms to the left:

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

We multiply parentheses

-3x^2+10x+6x+50-4=0

We add all the numbers together, and all the variables

-3x^2+16x+46=0

a = -3; b = 16; c = +46;
Δ = b2-4ac
Δ = 162-4·(-3)·46
Δ = 808
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:

$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{202}}{2*-3}=\frac{-16-2\sqrt{202}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{202}}{2*-3}=\frac{-16+2\sqrt{202}}{-6}
$