-(15x-5)(2x-1)=3(3x-5)

Solution for -(15x-5)(2x-1)=3(3x-5) equation:

-(15x-5)(2x-1)=3(3x-5)

We move all terms to the left:

-(15x-5)(2x-1)-(3(3x-5))=0

We multiply parentheses ..

-(+30x^2-15x-10x+5)-(3(3x-5))=0


We calculate terms in parentheses: -(3(3x-5)), so:

3(3x-5)

We multiply parentheses

9x-15

Back to the equation:

-(9x-15)


We get rid of parentheses

-30x^2+15x+10x-9x-5+15=0

We add all the numbers together, and all the variables

-30x^2+16x+10=0

a = -30; b = 16; c = +10;
Δ = b2-4ac
Δ = 162-4·(-30)·10
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{91}}{2*-30}=\frac{-16-4\sqrt{91}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{91}}{2*-30}=\frac{-16+4\sqrt{91}}{-60}
$