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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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


We calculate terms in parentheses: -((+2x^2+3x+4)), so:

(+2x^2+3x+4)

We get rid of parentheses

2x^2+3x+4

Back to the equation:

-(2x^2+3x+4)


We get rid of parentheses

5x^2-2x^2-3x-4-7=0

We add all the numbers together, and all the variables

3x^2-3x-11=0

a = 3; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·3·(-11)
Δ = 141
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{-(-3)-\sqrt{141}}{2*3}=\frac{3-\sqrt{141}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{141}}{2*3}=\frac{3+\sqrt{141}}{6}
$