5(-3x2)-(x-3)=-4(4x+5)+13

Solution for 5(-3x2)-(x-3)=-4(4x+5)+13 equation:

5(-3x^2)-(x-3)=-4(4x+5)+13

We move all terms to the left:

5(-3x^2)-(x-3)-(-4(4x+5)+13)=0

We multiply parentheses

-15x^2-(x-3)-(-4(4x+5)+13)=0

We get rid of parentheses

-15x^2-x-(-4(4x+5)+13)+3=0


We calculate terms in parentheses: -(-4(4x+5)+13), so:

-4(4x+5)+13

We multiply parentheses

-16x-20+13

We add all the numbers together, and all the variables

-16x-7

Back to the equation:

-(-16x-7)


We add all the numbers together, and all the variables

-15x^2-1x-(-16x-7)+3=0

We get rid of parentheses

-15x^2-1x+16x+7+3=0

We add all the numbers together, and all the variables

-15x^2+15x+10=0

a = -15; b = 15; c = +10;
Δ = b2-4ac
Δ = 152-4·(-15)·10
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{33}}{2*-15}=\frac{-15-5\sqrt{33}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{33}}{2*-15}=\frac{-15+5\sqrt{33}}{-30}
$