5x^2=7-3x

Solution for 5x^2=7-3x equation:

5x^2=7-3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5x^2+3x-7=0

a = 5; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·5·(-7)
Δ = 149
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{149}}{2*5}=\frac{-3-\sqrt{149}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*5}=\frac{-3+\sqrt{149}}{10}
$