3(x-1)+7=4x2-3(2-x)

Solution for 3(x-1)+7=4x2-3(2-x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4x^2-3(-1x+2)), so:

4x^2-3(-1x+2)

We multiply parentheses

4x^2+3x-6

Back to the equation:

-(4x^2+3x-6)


We add all the numbers together, and all the variables

3x-(4x^2+3x-6)+4=0

We get rid of parentheses

-4x^2+3x-3x+6+4=0

We add all the numbers together, and all the variables

-4x^2+10=0

a = -4; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-4)·10
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-4}=\frac{0-4\sqrt{10}}{-8}
=-\frac{4\sqrt{10}}{-8}
=-\frac{\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-4}=\frac{0+4\sqrt{10}}{-8}
=\frac{4\sqrt{10}}{-8}
=\frac{\sqrt{10}}{-2}
$