5(x2-7)=3(9-x2)+10

Solution for 5(x2-7)=3(9-x2)+10 equation:

5(x2-7)=3(9-x2)+10

We move all terms to the left:

5(x2-7)-(3(9-x2)+10)=0

We add all the numbers together, and all the variables

5(+x^2-7)-(3(-1x^2+9)+10)=0

We multiply parentheses

5x^2-(3(-1x^2+9)+10)-35=0


We calculate terms in parentheses: -(3(-1x^2+9)+10), so:

3(-1x^2+9)+10

We multiply parentheses

-3x^2+27+10

We add all the numbers together, and all the variables

-3x^2+37

Back to the equation:

-(-3x^2+37)


We get rid of parentheses

5x^2+3x^2-37-35=0

We add all the numbers together, and all the variables

8x^2-72=0

a = 8; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·8·(-72)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*8}=\frac{48}{16}
=3
$