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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-10x^2+14x+(3x+2)-(4x-2(x+3))=0

We get rid of parentheses

-10x^2+14x+3x-(4x-2(x+3))+2=0


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

4x-2(x+3)

We multiply parentheses

4x-2x-6

We add all the numbers together, and all the variables

2x-6

Back to the equation:

-(2x-6)


We add all the numbers together, and all the variables

-10x^2+17x-(2x-6)+2=0

We get rid of parentheses

-10x^2+17x-2x+6+2=0

We add all the numbers together, and all the variables

-10x^2+15x+8=0

a = -10; b = 15; c = +8;
Δ = b2-4ac
Δ = 152-4·(-10)·8
Δ = 545
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{-(15)-\sqrt{545}}{2*-10}=\frac{-15-\sqrt{545}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{545}}{2*-10}=\frac{-15+\sqrt{545}}{-20}
$