5x(x-3)-7=-2(x+4)+1

Solution for 5x(x-3)-7=-2(x+4)+1 equation:

5x(x-3)-7=-2(x+4)+1

We move all terms to the left:

5x(x-3)-7-(-2(x+4)+1)=0

We multiply parentheses

5x^2-15x-(-2(x+4)+1)-7=0


We calculate terms in parentheses: -(-2(x+4)+1), so:

-2(x+4)+1

We multiply parentheses

-2x-8+1

We add all the numbers together, and all the variables

-2x-7

Back to the equation:

-(-2x-7)


We get rid of parentheses

5x^2-15x+2x+7-7=0

We add all the numbers together, and all the variables

5x^2-13x=0

a = 5; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·5·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*5}=\frac{26}{10}
=2+3/5
$