x=(3x+10)(5x-26)

Solution for x=(3x+10)(5x-26) equation:

x=(3x+10)(5x-26)

We move all terms to the left:

x-((3x+10)(5x-26))=0

We multiply parentheses ..

-((+15x^2-78x+50x-260))+x=0


We calculate terms in parentheses: -((+15x^2-78x+50x-260)), so:

(+15x^2-78x+50x-260)

We get rid of parentheses

15x^2-78x+50x-260

We add all the numbers together, and all the variables

15x^2-28x-260

Back to the equation:

-(15x^2-28x-260)


We add all the numbers together, and all the variables

x-(15x^2-28x-260)=0

We get rid of parentheses

-15x^2+x+28x+260=0

We add all the numbers together, and all the variables

-15x^2+29x+260=0

a = -15; b = 29; c = +260;
Δ = b2-4ac
Δ = 292-4·(-15)·260
Δ = 16441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{16441}}{2*-15}=\frac{-29-\sqrt{16441}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{16441}}{2*-15}=\frac{-29+\sqrt{16441}}{-30}
$