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

Solution for 5(-3x-2)(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 ..

5(-3x^2+9x-2x+6)-(-4(4x+5)+13)=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 multiply parentheses

-15x^2+45x-10x-(-16x-7)+30=0

We get rid of parentheses

-15x^2+45x-10x+16x+7+30=0

We add all the numbers together, and all the variables

-15x^2+51x+37=0

a = -15; b = 51; c = +37;
Δ = b2-4ac
Δ = 512-4·(-15)·37
Δ = 4821
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{-(51)-\sqrt{4821}}{2*-15}=\frac{-51-\sqrt{4821}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{4821}}{2*-15}=\frac{-51+\sqrt{4821}}{-30}
$