17-5(2x-9)=-x(-6x+10)+4

Solution for 17-5(2x-9)=-x(-6x+10)+4 equation:

17-5(2x-9)=-x(-6x+10)+4

We move all terms to the left:

17-5(2x-9)-(-x(-6x+10)+4)=0

We multiply parentheses

-10x-(-x(-6x+10)+4)+45+17=0


We calculate terms in parentheses: -(-x(-6x+10)+4), so:

-x(-6x+10)+4

We multiply parentheses

6x^2-10x+4

Back to the equation:

-(6x^2-10x+4)


We add all the numbers together, and all the variables

-10x-(6x^2-10x+4)+62=0

We get rid of parentheses

-6x^2-10x+10x-4+62=0

We add all the numbers together, and all the variables

-6x^2+58=0

a = -6; b = 0; c = +58;
Δ = b2-4ac
Δ = 02-4·(-6)·58
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{87}}{2*-6}=\frac{0-4\sqrt{87}}{-12}
=-\frac{4\sqrt{87}}{-12}
=-\frac{\sqrt{87}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{87}}{2*-6}=\frac{0+4\sqrt{87}}{-12}
=\frac{4\sqrt{87}}{-12}
=\frac{\sqrt{87}}{-3}
$