-7+3x(x-5)=5x-2(9+x)-4

Solution for -7+3x(x-5)=5x-2(9+x)-4 equation:

-7+3x(x-5)=5x-2(9+x)-4

We move all terms to the left:

-7+3x(x-5)-(5x-2(9+x)-4)=0

We add all the numbers together, and all the variables

3x(x-5)-(5x-2(x+9)-4)-7=0

We multiply parentheses

3x^2-15x-(5x-2(x+9)-4)-7=0


We calculate terms in parentheses: -(5x-2(x+9)-4), so:

5x-2(x+9)-4

We multiply parentheses

5x-2x-18-4

We add all the numbers together, and all the variables

3x-22

Back to the equation:

-(3x-22)


We get rid of parentheses

3x^2-15x-3x+22-7=0

We add all the numbers together, and all the variables

3x^2-18x+15=0

a = 3; b = -18; c = +15;
Δ = b2-4ac
Δ = -182-4·3·15
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*3}=\frac{30}{6}
=5
$