15x(-6x+5)-2-(-x+3)=-(7x+23)-x+(3-2x)

Solution for 15x(-6x+5)-2-(-x+3)=-(7x+23)-x+(3-2x) equation:

15x(-6x+5)-2-(-x+3)=-(7x+23)-x+(3-2x)

We move all terms to the left:

15x(-6x+5)-2-(-x+3)-(-(7x+23)-x+(3-2x))=0

We add all the numbers together, and all the variables

15x(-6x+5)-(-1x+3)-(-(7x+23)-x+(-2x+3))-2=0

We multiply parentheses

-90x^2+75x-(-1x+3)-(-(7x+23)-x+(-2x+3))-2=0

We get rid of parentheses

-90x^2+75x+1x-(-(7x+23)-x+(-2x+3))-3-2=0


We calculate terms in parentheses: -(-(7x+23)-x+(-2x+3)), so:

-(7x+23)-x+(-2x+3)

We add all the numbers together, and all the variables

-1x-(7x+23)+(-2x+3)

We get rid of parentheses

-1x-7x-2x-23+3

We add all the numbers together, and all the variables

-10x-20

Back to the equation:

-(-10x-20)


We add all the numbers together, and all the variables

-90x^2+76x-(-10x-20)-5=0

We get rid of parentheses

-90x^2+76x+10x+20-5=0

We add all the numbers together, and all the variables

-90x^2+86x+15=0

a = -90; b = 86; c = +15;
Δ = b2-4ac
Δ = 862-4·(-90)·15
Δ = 12796
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:

$\sqrt{\Delta}=\sqrt{12796}=\sqrt{4*3199}=\sqrt{4}*\sqrt{3199}=2\sqrt{3199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{3199}}{2*-90}=\frac{-86-2\sqrt{3199}}{-180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{3199}}{2*-90}=\frac{-86+2\sqrt{3199}}{-180}
$